User:Salix alba/maths2018

These statistics are from analysis of all mathematical and chemical formula from the June 2018 dump

=Maths equations per wiki=

Top 20

  • 1050627 enwiki
  • 633916 dewiki
  • 347959 frwiki
  • 345277 enwikiversity
  • 309154 ruwiki
  • 207547 itwiki
  • 205233 enwikibooks
  • 181745 zhwiki
  • 166130 frwikiversity
  • 165819 eswiki
  • 153952 ptwiki
  • 148956 plwiki
  • 144897 ukwiki
  • 139353 jawiki
  • 135909 kowiki
  • 133368 dewikibooks
  • 129413 hewiki
  • 97290 enwikisource
  • 82504 frwikisource
  • 78378 cawiki

=Pages with maths equation per wiki=

  • 63793 enwiki
  • 33066 dewiki
  • 20120 frwiki
  • 19961 ruwiki
  • 11566 jawiki
  • 11060 zhwiki
  • 10930 eswiki
  • 10782 itwiki
  • 9051 plwiki
  • 8274 ptwiki
  • 7752 hewiki
  • 7422 ukwiki
  • 7190 nlwiki
  • 6932 enwikisource
  • 6832 frwikisource
  • 6735 srwiki
  • 6303 enwikiversity
  • 6128 enwikibooks
  • 5628 shwiki
  • 5364 commonswiki

= Equations per namespace =

5040531 0 (Article)

237333 1 Talk:

752712 2 User:

64742 3 User Talk:

105637 4

7321 5

16263 6

396 7

294 8

137 9

12817 10

1290 11

36485 12

1183 13

263 14

359 15

64 90

7205 100

2189 101

65076 102

1499 103

183049 104

540 105

32903 106

337 107

15049 108

42 109

458 110

1 111

530 113

7237 114

31 115

41 116

4466 118

3 119

32 121

28 200

362 202

24 203

8491 250

11 447

425 828

7 829

820 1198

=Opening tags =

  • 5588629
  • 859406 :
  • 74653 ::
  • 17967
  • 9790 :::
  • 9154
  • 7759
  • 6066
  • 5836
  • 4961 ::::
  • 4254
  • 2342 :::::
  • 1646 ::::::
  • 1460 :
  • 933
  • 728
  • 647 :
  • 637 :
  • 590
  • 586 :::::::

= Most common equations =

49692 n

43553 A

42323 x

33946 f

32490 X

29502 a

22383 p

21077 k

20517 G

19840 B

19505 M

17476 \rightleftharpoons

17313 \alpha

17213 m

16905 S

16515 R

16304 b

15893 P

15419 y

14781 i

14690 K

14522 V

14242 t

14217 r

13658 T

13035 c

12259 N

11852 F

11380 E

11325 C

10698 \lambda

10486 L

10311 v

10242 g

9678 \mu

9132 1

8913 0

8825 H

8777 q

8744 Y

8657 d

8597 \theta

8370

8354 D

8336 I

8150 z

8112 h

8054 \phi

7903 \pi

7766 U

7757 s

7565 Q

7557 \beta

7483 \sigma

7314 u

7179 \omega

7169 \rho

6950 \gamma

6660 \varphi

6390 f(x)

6338 e

6232 \Omega

5315 \tau

5008 l

4810 \mathfrak{P}

4755 j

4589 x_0

4496 \delta

4436 W

4433 \mathbb{R}

4335 \epsilon

4316 w

4265 \R

4047 \nu

3940 {\mathbb {\color{Blue}_{DMY} } }

3854 \varepsilon

3735 \psi

3583 2

3483 \Gamma

3398 x_i

3392 Z

3374 \

3361 \infty

3146 \Phi

3111 \Rightarrow

3067 \rightarrow

3040 \Sigma

2838 \Delta

2808 O

2792 +

2721 =

2699 \kappa

2605 \mathbb{C}

2554 \lbrack\alpha\rbrack_{D}^{25}

2550 \eta

2518 x_1

2385 \cdot

2306 \mathbb{R}^n

2287 \sim

2284 \mathbb{N}

2230 \sqrt{2}

2214 \xi

2186 [a,b]

2181 J

2176 A

2121 3

2095 \R^n

2001 x

1921 \ell

1914 n

1879 \mathbb{Z}

1873 -1

1844 \mathbb{Q}

1832 a_n

1831 \hbar

1825 \mathcal{A}

1821 o

1767 \times

1751 \mathfrak{p}

1693 x_2

1693 -

1672 \mathcal{F}

1654 x=0

1615 X

1604 \chi

1600 \varnothing

1599 \mathfrak{g}

1579 a_i

1573 n-1

1573 \Lambda

1530 \mathbb R

1514 \to

1497 AB

1474 f

1443 p_i

1440 \color{Red} \oplus

1437 \in

1429 \Leftrightarrow

1420 ','

1409 \mathcal{C}

1405 2\pi

1397 \flat

1394 \land

1385 \mathcal C

1380 \mathbf{A}

1353 X_i

1352 4

1322 H_0

1279 \aleph_0

1265 \alpha

1229 \Delta t

1217 \zeta

1217 n+1

1212 A_i

1209 2^n

1208 \Complex

1203 A_1

1187 a_1

1183 \nabla

1180 x\in X

1177 -\infty

1175 \frac{1}{2}

1165 x(t)

1164 \Z

1138 z_0

1134 +\infty

1132 \mathcal{H}

1130 t_0

1129 \mathbf{x}

1111 x_n

1096 g(x)

1095 P_1

1094 (x,y)

1086 (a,b)

1083 \Delta x

1072 T_1

1071 \oplus

1062 n=1

1061 \N

1060 5

1056 \longrightarrow

1045 \mathbb{R}^3

1045 \circ

1040 *

1037 a

1035 S_n

1026 O(n)

1021 \textit{n}_{D}^{20}

1002 x\,

Alternatives

  • {{tag|math|o}} n inline text — {{tl|mvar}} {{mvar|n}} inline text
  • {{tag|math|o}} A inline text — {{tl|mvar}} {{mvar|A}} inline text
  • {{tag|math|o}} \alpha inline text — {{tl|mvar}} {{mvar|α}} inline text
  • {{tag|math|o}} \pi inline text — {{tl|mvar}} {{mvar|π}} inline text

Some really big equations

\begin{align} &\left(\frac{\partial^2}{\partial r^2} +\frac{2}{r}\frac{\partial}{\partial r} +\frac{1}{r^2}\frac{\partial^2}{\partial\theta^2} +\frac{1}{r^2\tan\theta }\frac{\partial}{\partial\theta} +\frac{1}{r^2\sin^2\theta}\frac{\partial^2}{\partial\varphi^2} \right)\cdot (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) \\=& \frac{\partial^2}{\partial r^2} (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) +\frac{2}{r}\frac{\partial}{\partial r} (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) +\frac{1}{r^2}\frac{\partial^2}{\partial\theta^2} (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) \\& +\frac{1}{r^2\tan\theta }\frac{\partial}{\partial\theta} (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) +\frac{1}{r^2\sin^2\theta}\frac{\partial^2}{\partial\varphi^2} (v_r\hat{e}_r +v_\theta\hat{e}_\theta+v_\varphi\hat{e}_\varphi) \\=& v_{r,rr}\hat{e}_r +v_{\theta,rr}\hat{e}_\theta+v_{\varphi,rr}\hat{e}_\varphi +\frac{2}{r}v_{r,r}\hat{e}_r +\frac{2}{r}v_{\theta,r}\hat{e}_\theta+\frac{2}{r}v_{\varphi,r}\hat{e}_\varphi \\& +\frac{1}{r^2}\frac{\partial}{\partial\theta} ( v_{r,\theta}\hat{e}_r +v_r\hat{e}_\theta +v_{\theta,\theta}\hat{e}_\theta -v_\theta\hat{e}_r +v_{\varphi,\theta}\hat{e}_\varphi ) \\& +\frac{1}{r^2\tan\theta} ( v_{r,\theta}\hat{e}_r +v_r\hat{e}_\theta +v_{\theta,\theta}\hat{e}_\theta -v_\theta\hat{e}_r +v_{\varphi,\theta}\hat{e}_\varphi ) \\& +\frac{1}{r^2\sin^2\theta}\frac{\partial}{\partial\varphi} ( v_{r,\varphi}\hat{e}_r +\sin\theta v_r\hat{e}_\varphi +v_{\theta,\varphi}\hat{e}_\theta +\cos\theta v_\theta\hat{e}_\varphi +v_{\varphi,\varphi}\hat{e}_\varphi -\sin\theta v_\varphi\hat{e}_r -\cos\theta v_\varphi\hat{e}_{\theta} ) \\=& v_{r,rr}\hat{e}_r +v_{\theta,rr}\hat{e}_\theta+v_{\varphi,rr}\hat{e}_\varphi +\frac{2}{r}v_{r,r}\hat{e}_r +\frac{2}{r}v_{\theta,r}\hat{e}_\theta+\frac{2}{r}v_{\varphi,r}\hat{e}_\varphi \\& +\frac{1}{r^2} ( v_{r,\theta\theta}\hat{e}_r +v_{r,\theta}\hat{e}_\theta +v_{r,\theta}\hat{e}_\theta -v_r\hat{e}_r +v_{\theta,\theta\theta}\hat{e}_\theta -v_{\theta,\theta}\hat{e}_r -v_{\theta,\theta}\hat{e}_r -v_\theta\hat{e}_\theta +v_{\varphi,\theta\theta}\hat{e}_\varphi ) \\& +\frac{1}{r^2\tan\theta}( v_{r,\theta}\hat{e}_r +v_r\hat{e}_\theta +v_{\theta,\theta}\hat{e}_\theta -v_\theta\hat{e}_r +v_{\varphi,\theta}\hat{e}_\varphi ) \\& +\frac{1}{r^2\sin^2\theta} ( v_{r,\varphi\varphi}\hat{e}_r +\sin\theta v_{r,\varphi}\hat{e}_\varphi +\sin\theta v_{r,\varphi}\hat{e}_\varphi -\sin^2\theta v_r\hat{e}_r -\sin\theta\cos\theta v_r\hat{e}_\theta \\& +v_{\theta,\varphi\varphi}\hat{e}_\theta +\cos\theta v_{\theta,\varphi}\hat{e}_\varphi +\cos\theta v_{\theta,\varphi}\hat{e}_\varphi -\sin\theta\cos\theta v_\theta\hat{e}_r -\cos^2\theta v_\theta\hat{e}_\theta \\& +v_{\varphi,\varphi\varphi}\hat{e}_\varphi -\sin\theta v_{\varphi,\varphi}\hat{e}_r -\cos\theta v_{\varphi,\varphi}\hat{e}_\theta -\sin\theta v_{\varphi,\varphi}\hat{e}_r -\sin^2\theta v_\varphi\hat{e}_\varphi \\& -\cos\theta v_{\varphi,\varphi}\hat{e}_\theta -\cos^2\theta v_\varphi\hat{e}_\varphi ) \\=& \Bigl( v_{r,rr} +\frac{2}{r}v_{r,r} +\frac{1}{r^2}v_{r,\theta\theta} +\frac{1}{r^2\tan\theta}v_{r,\theta} +\frac{1}{r^2\sin^2\theta}v_{r,\varphi\varphi} \\&\qquad -\frac{1}{r^2}v_r -\frac{1}{r^2}v_{\theta,\theta} -\frac{1}{r^2}v_{\theta,\theta} -\frac{1}{r^2\tan\theta}v_\theta -\frac{1}{r^2}v_r -\frac{\cos\theta}{r^2\sin\theta}v_\theta -\frac{1}{r^2\sin\theta}v_{\varphi,\varphi} -\frac{1}{r^2\sin\theta}v_{\varphi,\varphi} \Bigr)\hat{e}_r \\& +\Bigl( v_{\theta,rr} +\frac{2}{r}v_{\theta,r} +\frac{1}{r^2}v_{\theta,\theta\theta} +\frac{1}{r^2\tan\theta}v_{\theta,\theta} +\frac{1}{r^2\sin^2\theta}v_{\theta,\varphi\varphi} \\&\qquad +\frac{2}{r^2}v_{r,\theta} -\frac{1}{r^2}v_\theta +\frac{1}{r^2\tan\theta}v_r -\frac{\cos\theta}{r^2\sin\theta}v_r -\frac{\cos^2\theta}{r^2\sin^2\theta}v_\theta -\frac{2\cos\theta}{r^2\sin^2\theta}v_{\varphi,\varphi} \Bigr)\hat{e}_\theta \\& +\Bigl( v_{\varphi,rr} +\frac{2}{r}v_{\varphi,r} +\frac{1}{r^2}v_{\varphi,\theta\theta} +\frac{1}{r^2\tan\theta}v_{\varphi,\theta} +\frac{1}{r^2\sin^2\theta}v_{\varphi,\varphi\varphi} \\&\qquad +\frac{2}{r^2\sin\theta}v_{r,\varphi} +\frac{2\cos\theta}{r^2\sin^2\theta}v_{\theta,\varphi} -\frac{\sin^2\theta+\cos^2\theta}{r^2\sin^2\theta}v_\varphi \Bigr)\hat{e}_\varphi \\=& \left( \Delta v_r -\frac{2}{r^2}v_r -\frac{2}{r^2}v_{\theta,\theta} -\frac{2}{r^2\tan\theta}v_\theta -\frac{2}{r^2\sin\theta}v_{\varphi,\varphi} \right)\hat{e}_r \\& +\left( \Delta v_\theta +\frac{2}{r^2}v_{r,\theta} -\frac{1}{r^2\sin^2\theta}v_\theta -\frac{2\cos\theta}{r^2\sin^2\theta}v_{\varphi,\varphi} \right)\hat{e}_\theta \\& +\left( \Delta v_\varphi +\frac{2\cos\theta}{r^2\sin^2\theta}v_{\theta,\varphi} -\frac{1}{r^2\sin^2\theta}v_\varphi +\frac{2}{r^2\sin\theta}v_{r,\varphi} \right)\hat{e}_\varphi \end{align},

\begin{array}{r|l|l|l} n & \sin\left(\frac{2\pi}{n}\right) & \cos\left(\frac{2\pi}{n}\right) & \tan\left(\frac{2\pi}{n}\right) \\ \hline 1 & 0 & 1 & 0 \\ \hline 2 & 0 & -1 & 0 \\ \hline 3 & \frac{1}{2}\sqrt{3} & -\frac{1}{2} & -\sqrt{3} \\ \hline 4 & 1 & 0 & \pm\infty \\ \hline 5 & \frac{1}{4}\left(\sqrt{10+2\sqrt{5}}\right) & \frac{1}{4}\left(\sqrt{5}-1\right) & \sqrt{5+2\sqrt{5}} \\ \hline 6 & \frac{1}{2}\sqrt{3} & \frac{1}{2} & \sqrt{3} \\ \hline 7 & \frac{1}{2}\sqrt{\frac{1}{3}\left(7-\omega^2\sqrt[3]{\frac{7+21\sqrt{-3}}{2}}-\omega\sqrt[3]{\frac{7-21\sqrt{-3}}{2}}\right)} & \frac{1}{6}\left(-1+\sqrt[3]{\frac{7+21\sqrt{-3}}{2}}+\sqrt[3]{\frac{7-21\sqrt{-3}}{2}}\right) & \\ \hline 8 & \frac{1}{2}\sqrt{2} & \frac{1}{2}\sqrt{2} & 1 \\ \hline 9 & \frac{1}{4}\left(\sqrt[3]{4(-1+\sqrt{-3})}+\sqrt[3]{4(-1-\sqrt{-3})}\right) & & \\ \hline 10 & \frac{1}{4}\left(\sqrt{10-2\sqrt{5}}\right) & \frac{1}{4}\left(\sqrt{5}+1\right) & \sqrt{5-2\sqrt{5}} \\ \hline 11 & & & \\ \hline 12 & \frac{1}{2} & \frac{1}{2}\sqrt{3} & \frac{1}{3}\sqrt{3} \\ \hline 13 & & & \\ \hline 14 & \frac{1}{24}\sqrt{3\left(112-\sqrt[3]{14336+\sqrt{-5549064193}}-\sqrt[3]{14336-\sqrt{-5549064193}}\right)} & \frac{1}{24}\sqrt{3\left(80+\sqrt[3]{14336+\sqrt{-5549064193}}+\sqrt[3]{14336-\sqrt{-5549064193}}\right)} & \sqrt{\frac{112-\sqrt[3]{14336+\sqrt{-5549064193}}-\sqrt[3]{14336-\sqrt{-5549064193}}}{80+\sqrt[3]{14336+\sqrt{-5549064193}}+\sqrt[3]{14336-\sqrt{-5549064193}}}} \\ \hline 15 & \frac{1}{8}\left(\sqrt{15}+\sqrt{3}-\sqrt{10-2\sqrt{5}}\right) & \frac{1}{8}\left(1+\sqrt{5}+\sqrt{30-6\sqrt{5}}\right) & \frac{1}{2}\left(-3\sqrt{3}-\sqrt{15}+\sqrt{50+22\sqrt{5}}\right) \\ \hline 16 & \frac{1}{2}\left(\sqrt{2-\sqrt{2}}\right) & \frac{1}{2}\left(\sqrt{2+\sqrt{2}}\right) & \sqrt{2}-1 \\ \hline 17 & & \frac{1}{16}\left(-1+\sqrt{17}+\sqrt{34-2\sqrt{17}}+2\sqrt{17+3\sqrt{17}-\sqrt{34-2\sqrt{17}}-2\sqrt{34+2\sqrt{17}}}\right) & \\ \hline 18 & \frac{1}{4}\left(\sqrt[3]{4\sqrt{-1}-4\sqrt{3}}-\sqrt[3]{4\sqrt{-1}+4\sqrt{3}}\right) & \frac{1}{4}\left(\sqrt[3]{4+4\sqrt{-3}}+\sqrt[3]{4-4\sqrt{-3}}\right) & \\ \hline 19 & & & \\ \hline 20 & \frac{1}{4}\left(\sqrt{5}-1\right) & \frac{1}{4}\left(\sqrt{10+2\sqrt{5}}\right) & \frac{1}{5}\left(\sqrt{25-10\sqrt{5}}\right) \\ \hline 21 & & & \\ \hline 22 & & & \\ \hline 23 & & & \\ \hline 24 & \frac{1}{4}\left(\sqrt{6}-\sqrt{2}\right) & \frac{1}{4}\left(\sqrt{6}+\sqrt{2}\right) & 2-\sqrt{3} \end{array}

P_{5}(x|q)=1+ \left( 1-{q}^{-5} \right) \left( 1-{q}^{-4} \right) \left( 1-{q}^ {-3} \right) \left( 1-{q}^{6} \right) \left( 1-{q}^{7} \right) \left( 1-{q}^{8} \right) \left( 1-\sqrt [4]{q} \left( x+i\sqrt {1-{x }^{2}} \right) \right) \left( 1-{q}^{5/4} \left( x+i\sqrt {1-{x}^{2} } \right) \right) \left( 1-{q}^{9/4} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{\frac {\sqrt [4]{q}}{x+i\sqrt {1-{x}^{2}} }} \right) \left( 1-{\frac {{q}^{5/4}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{\frac {{q}^{9/4}}{x+i\sqrt {1-{x}^{2}}}} \right) { q}^{3} \left( 1-q \right) ^{-2} \left( 1-{q}^{2} \right) ^{-2} \left( 1-{q}^{3} \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+{q}^ {3/2} \right) ^{-1} \left( 1+{q}^{5/2} \right) ^{-1} \left( 1+q \right) ^{-1} \left( 1+{q}^{2} \right) ^{-1} \left( 1+{q}^{3} \right) ^{-1}+ \left( 1-{q}^{-5} \right) \left( 1-{q}^{-4} \right) \left( 1-{q}^{-3} \right) \left( 1-{q}^{-2} \right) \left( 1-{q}^{6 } \right) \left( 1-{q}^{7} \right) \left( 1-{q}^{8} \right) \left( 1-{q}^{9} \right) \left( 1-\sqrt [4]{q} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{5/4} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{9/4} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{{\frac {13}{4}}} \left( x+i\sqrt {1-{ x}^{2}} \right) \right) \left( 1-{\frac {\sqrt [4]{q}}{x+i\sqrt {1-{ x}^{2}}}} \right) \left( 1-{\frac {{q}^{5/4}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{\frac {{q}^{9/4}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{q}^{{\frac {13}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) ^{ -1} \right) {q}^{4} \left( 1-q \right) ^{-2} \left( 1-{q}^{2} \right) ^{-2} \left( 1-{q}^{3} \right) ^{-2} \left( 1-{q}^{4} \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+{q}^{3/2} \right) ^{-1} \left( 1+{q}^{5/2} \right) ^{-1} \left( 1+{q}^{7/2} \right) ^{-1} \left( 1+q \right) ^{-1} \left( 1+{q}^{2} \right) ^{-1} \left( 1+{q}^ {3} \right) ^{-1} \left( 1+{q}^{4} \right) ^{-1}+ \left( 1-{q}^{-5} \right) \left( 1-{q}^{-4} \right) \left( 1-{q}^{-3} \right) \left( 1-{q}^{-2} \right) \left( 1-{q}^{-1} \right) \left( 1-{q}^{6 } \right) \left( 1-{q}^{7} \right) \left( 1-{q}^{8} \right) \left( 1-{q}^{9} \right) \left( 1-{q}^{10} \right) \left( 1-\sqrt [4]{q} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{5/4} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{9/4} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{{\frac { 13}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{{ \frac {17}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) \right) \left( 1 -{\frac {\sqrt [4]{q}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{ \frac {{q}^{5/4}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{\frac {{q} ^{9/4}}{x+i\sqrt {1-{x}^{2}}}} \right) \left( 1-{q}^{{\frac {13}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) ^{-1} \right) \left( 1-{q}^{{ \frac {17}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) ^{-1} \right) {q}^ {5} \left( 1-q \right) ^{-2} \left( 1-{q}^{2} \right) ^{-2} \left( 1-{ q}^{3} \right) ^{-2} \left( 1-{q}^{4} \right) ^{-2} \left( 1-{q}^{5} \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+{q}^{3/2} \right) ^{-1} \left( 1+{q}^{5/2} \right) ^{-1} \left( 1+{q}^{7/2} \right) ^{-1} \left( 1+{q}^{9/2} \right) ^{-1} \left( 1+q \right) ^{- 1} \left( 1+{q}^{2} \right) ^{-1} \left( 1+{q}^{3} \right) ^{-1} \left( 1+{q}^{4} \right) ^{-1} \left( 1+{q}^{5} \right) ^{-1}-{\frac {{q}^{5/4}}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) \left( x+i\sqrt {1-{x}^{2}} \right) }}-{\frac {{q }^{5/4} \left( x+i\sqrt {1-{x}^{2}} \right) }{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}+{q}^{{\frac {29}{4} }} \left( 1-q \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+ q \right) ^{-1} \left( x+i\sqrt {1-{x}^{2}} \right) ^{-1}+{q}^{{\frac {29}{4}}} \left( x+i\sqrt {1-{x}^{2}} \right) \left( 1-q \right) ^{-2 } \left( 1+\sqrt {q} \right) ^{-1} \left( 1+q \right) ^{-1}+{q}^{-{ \frac {15}{4}}} \left( 1-q \right) ^{-2} \left( 1+\sqrt {q} \right) ^{ -1} \left( 1+q \right) ^{-1} \left( x+i\sqrt {1-{x}^{2}} \right) ^{-1} + \left( x+i\sqrt {1-{x}^{2}} \right) {q}^{-{\frac {15}{4}}} \left( 1- q \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+q \right) ^{ -1}-{\frac {{q}^{9/4}}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) \left( x+i\sqrt {1-{x}^{2}} \right) }}-{ \frac {{q}^{9/4} \left( x+i\sqrt {1-{x}^{2}} \right) }{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}+ \left( 1-{q}^{-5} \right) \left( 1-{q}^{-4} \right) \left( 1-{q}^{6 } \right) \left( 1-{q}^{7} \right) \left( 1-\sqrt [4]{q} \left( x+i \sqrt {1-{x}^{2}} \right) \right) \left( 1-{q}^{5/4} \left( x+i \sqrt {1-{x}^{2}} \right) \right) \left( 1-{\frac {\sqrt [4]{q}}{x+i \sqrt {1-{x}^{2}}}} \right) \left( 1-{\frac {{q}^{5/4}}{x+i\sqrt {1-{ x}^{2}}}} \right) {q}^{2} \left( 1-q \right) ^{-2} \left( 1-{q}^{2} \right) ^{-2} \left( 1+\sqrt {q} \right) ^{-1} \left( 1+{q}^{3/2} \right) ^{-1} \left( 1+q \right) ^{-1} \left( 1+{q}^{2} \right) ^{-1} +{\frac {q}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}+{\frac {{q}^{3/2}}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}-{\frac {{q}^{7}}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}-{\frac {{q}^{15/2}}{ \left( 1-q \right) ^{2} \left( 1+ \sqrt {q} \right) \left( 1+q \right) }}-{\frac {1}{{q}^{4} \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}-{ \frac {1}{{q}^{7/2} \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}+{\frac {{q}^{2}}{ \left( 1-q \right) ^ {2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}+{\frac {{q}^{5/2 }}{ \left( 1-q \right) ^{2} \left( 1+\sqrt {q} \right) \left( 1+q \right) }}\cdots

\begin{align} \begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}^n \begin{pmatrix} f(0) \\ f(1) \end{pmatrix} & = A^n \begin{pmatrix} f(0) \\ f(1) \end{pmatrix} = \left(TDT^{-1}\right)^n \begin{pmatrix} f(0) \\ f(1) \end{pmatrix} = TD^nT^{-1} \begin{pmatrix} 0 \\ 1 \end{pmatrix}\\ &= \begin{pmatrix} \frac{-1-\sqrt{5}}{2} & \frac{-1+\sqrt{5}}{2}\\ 1 & 1 \end{pmatrix} \begin{pmatrix} \frac{1-\sqrt{5}}{2} & 0 \\ 0 & \frac{1+\sqrt{5}}{2} \end{pmatrix}^n \begin{pmatrix} -\frac{1}{\sqrt{5}} & \frac{\sqrt{5}-1}{2\sqrt{5}} \\ \frac{1}{\sqrt{5}} & \frac{\sqrt{5}+1}{2\sqrt{5}} \end{pmatrix} \begin{pmatrix} 0 \\ 1 \end{pmatrix}\\ &= \begin{pmatrix} \frac{-1-\sqrt{5}}{2} & \frac{-1+\sqrt{5}}{2}\\ 1 & 1 \end{pmatrix} \begin{pmatrix} \left(\frac{1-\sqrt{5}}{2}\right)^n & 0 \\ 0 & \left(\frac{1+\sqrt{5}}{2}\right)^n \end{pmatrix} \begin{pmatrix} -\frac{1}{\sqrt{5}} & \frac{\sqrt{5}-1}{2\sqrt{5}} \\ \frac{1}{\sqrt{5}} & \frac{\sqrt{5}+1}{2\sqrt{5}} \end{pmatrix} \begin{pmatrix} 0 \\ 1 \end{pmatrix}\\ &= \begin{pmatrix} \frac{-1-\sqrt{5}}{2}\left(\frac{1-\sqrt{5}}{2}\right)^n & \frac{-1+\sqrt{5}}{2}\left(\frac{1+\sqrt{5}}{2}\right)^n\\ \left(\frac{1-\sqrt{5}}{2}\right)^n & \left(\frac{1+\sqrt{5}}{2}\right)^n \end{pmatrix} \begin{pmatrix} \frac{\sqrt{5}-1}{2\sqrt{5}} \\ \frac{\sqrt{5}+1}{2\sqrt{5}} \end{pmatrix}\\ &= \begin{pmatrix} - \frac{1}{\sqrt{5}} \left(\frac{1-\sqrt{5}}{2}\right)^n + \frac{1}{\sqrt{5}} \left(\frac{1+\sqrt{5}}{2}\right)^n\\ - \frac{1}{\sqrt{5}} \left(\frac{1-\sqrt{5}}{2}\right)\left(\frac{1-\sqrt{5}}{2}\right)^n + \frac{1}{\sqrt{5}} \left(\frac{1+\sqrt{5}}{2}\right) \left(\frac{1+\sqrt{5}}{2}\right)^n \end{pmatrix} \\ &= \begin{pmatrix} \frac{1}{\sqrt{5}} \left[\left(\frac{1+\sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n\right]\\ \frac{1}{\sqrt{5}} \left[\left(\frac{1+\sqrt{5}}{2}\right)^{n+1} - \left(\frac{1-\sqrt{5}}{2}\right)^{n+1}\right] \end{pmatrix} \\ &= \begin{pmatrix} f(n) \\ f(n+1) \end{pmatrix} \end{align}

  • 78 ru:Процесс Грама ― Шмидта \begin{array}{l} \mathbf{b}_j\\ \\ \mathbf{b}_j \end{array} \begin{array}{c} = \\ \\ = \end{array} \underbrace{ \underbrace{ \underbrace{ \begin{array}{c} \mathbf{a}_j \\ \\ \mathbf{a}_j \end{array} \begin{array}{c} - \\ \\ - \end{array} \begin{array}{c} \mathbf{proj}_{\mathbf{b}_1}\,\mathbf{a}_j \\ || \\ \mathbf{proj}_{\mathbf{b}_1}\,\mathbf{a}_j \end{array} }_{\mathbf{a}_j^{(1)}} \begin{array}{c} - \\ \\ - \end{array} \begin{array}{c} \mathbf{proj}_{\mathbf{b}_2}\,\mathbf{a}_j \\ || \\ \mathbf{proj}_{\mathbf{b}_2}\,\mathbf{a}_j^{(1)} \end{array} }_{\mathbf{a}_j^{(2)}} \begin{array}{c} - \\ \\ - \end{array} \begin{array}{c} \mathbf{proj}_{\mathbf{b}_3}\,\mathbf{a}_j \\ || \\ \mathbf{proj}_{\mathbf{b}_3}\,\mathbf{a}_j^{(2)} \end{array} }_{\mathbf{a}_j^{(3)}} \begin{array}{ccc} - & \ldots & - \\ \\ - & \ldots & - \end{array} \begin{array}{cc} \mathbf{proj}_{\mathbf{b}_{j-1}}\,\mathbf{a}_j & (14) \\ || & \\ \mathbf{proj}_{\mathbf{b}_{j-1}}\,\mathbf{a}_j^{(j-2)} & (15) \end{array}
  • 73 :es:Matriz de adjuntos

\mbox{cof}(\mathbf{A}) = \begin{pmatrix} + \left | \begin{matrix} A_{22} & A_{23} \\ A_{32} & A_{33} \end{matrix} \right | & - \left | \begin{matrix} A_{21} & A_{23} \\ A_{31} & A_{33} \end{matrix} \right | & + \left | \begin{matrix} A_{21} & A_{22} \\ A_{31} & A_{32} \end{matrix} \right | \\ & & \\ - \left | \begin{matrix} A_{12} & A_{13} \\ A_{32} & A_{33} \end{matrix} \right | & + \left | \begin{matrix} A_{11} & A_{13} \\ A_{31} & A_{33} \end{matrix} \right | & - \left | \begin{matrix} A_{11} & A_{12} \\ A_{31} & A_{32} \end{matrix} \right| \\ & & \\ + \left | \begin{matrix} A_{12} & A_{13} \\ A_{22} & A_{23} \end{matrix} \right | & - \left | \begin{matrix} A_{11} & A_{13} \\ A_{21} & A_{23} \end{matrix} \right | & + \left | \begin{matrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix} \right| \end{pmatrix} = \begin{pmatrix} A_{22}A_{33} - A_{23}A_{32} & A_{23}A_{31} - A_{21}A_{33} & A_{21}A_{32} - A_{22}A_{31}\\ A_{32}A_{13} - A_{33}A_{12} & A_{33}A_{11} - A_{31}A_{13} & A_{31}A_{12} - A_{32}A_{11}\\ A_{12}A_{23} - A_{13}A_{22} & A_{13}A_{21} - A_{11}A_{23} & A_{11}A_{22} - A_{12}A_{21} \end{pmatrix}

\begin{matrix} \ \ 1 \ \ 8 \ \ \ 6 \ \ .8 \ \ 9 \\ \sqrt{ 3 \ 49 \ 27 \ .87 \ 21 } \\ & & & & & x=0\ \ \ \ & 20x+a \equiv \underline{a}\ \ \ \ \\ \underline{\ } \ 3 \qquad \qquad \quad \ & \underline{a} \times \underline{a} \le 3\ \\ \ \underline{\ 1 \ }\qquad \qquad \quad & \underline{1} \times \underline{1} = 1\ & \Rightarrow & a = 1 & \Rightarrow & x=\underline{1}\ \ \ \ & 20x+a \equiv 2 \underline{a}\ \ \ \\ \underline{\ } \ 2 \ 49 \qquad \qquad & 2\underline{a} \times \underline{a} \le 249 \\ \underline{\ 2 \ 24 \ } \quad \qquad \ & 2\underline{8} \times \underline{8} = 224 & \Rightarrow & a = 8 & \Rightarrow & x=1 \underline{8} \ \ \ & 20x+a \equiv 36 \underline{a}\ \ \\ \underline{\ } \ 25 \ 27 \qquad & 36\underline{a} \times \underline{a} \le 2527 \\ \ \ \underline{\ 21\ 96\ } \qquad & 36\underline{6} \times \underline{6} = 2196 & \Rightarrow & a = 6 & \Rightarrow & x=18\underline{6}\ \ & 20x+a \equiv 372 \underline{a}\ \\ \ \underline{\ } \ 3 \ 31 \ .87 & 372\underline{a} \times \underline{a} \le 33187 \\ \ \ \ \underline{\ 2 \ 98 \ .24\ } & 372\underline{8} \times \underline{8} = 29824 & \Rightarrow & a = 8 & \Rightarrow & x=186 \underline{8}\ & 20x+a \equiv 3736\underline{a} \\ \qquad \ \ \underline{\ } \ 33 \ .63 \ 21 & 3736\underline{a} \times \underline{a} \le 336321 \\ \qquad \ \quad \underline{\ 33 \ .63 \ 21\ } & 3736\underline{9} \times \underline{9} = 336321 & \Rightarrow & a = 9 & \Rightarrow & x=1868 \underline{9} \\ \qquad \qquad \qquad \ \ 0 \\ \end{matrix}

\mbox{adj}(\mathbf{A}) = \begin{pmatrix} + \left | \begin{matrix} A_{22} & A_{23} \\ A_{32} & A_{33} \end{matrix} \right | & - \left | \begin{matrix} A_{21} & A_{23} \\ A_{31} & A_{33} \end{matrix} \right | & + \left | \begin{matrix} A_{21} & A_{22} \\ A_{31} & A_{32} \end{matrix} \right | \\ & & \\ - \left | \begin{matrix} A_{12} & A_{13} \\ A_{32} & A_{33} \end{matrix} \right | & + \left | \begin{matrix} A_{11} & A_{13} \\ A_{31} & A_{33} \end{matrix} \right | & - \left | \begin{matrix} A_{11} & A_{12} \\ A_{31} & A_{32} \end{matrix} \right| \\ & & \\ + \left | \begin{matrix} A_{12} & A_{13} \\ A_{22} & A_{23} \end{matrix} \right | & - \left | \begin{matrix} A_{11} & A_{13} \\ A_{21} & A_{23} \end{matrix} \right | & + \left | \begin{matrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix} \right| \end{pmatrix}^T

\left\{\begin{matrix} \vdots \\ c^2[\frac{2}{1}]\\ c^1[\frac{1}{1}] \end{matrix}\right\}\subseteq \left\{\begin{matrix} \vdots \\ c^2[\frac{2}{1}]\\ c^1[\frac{1}{1}] \end{matrix}\right\},~ \left\{\begin{matrix} \vdots \\ c^2[\frac{4}{2}]\\ c^1[\frac{2}{2}] \end{matrix}\right\}\subset \left\{\begin{matrix} \vdots \\ c^2[\frac{4}{2}]\\ g^1[\frac{3}{2}]\\ c^1[\frac{2}{2}]\\ ~~c[\frac{1}{2}] \end{matrix}\right\},~ \left\{\begin{matrix} \vdots \\ c^2[\frac{6}{3}]\\ c^1[\frac{3}{3}] \end{matrix}\right\}\subset \left\{\begin{matrix} \vdots \\ c^2[\frac{6}{3}]\\ a^1[\frac{5}{3}]\\ f^1[\frac{4}{3}]\\ c^1[\frac{3}{3}]\\ ~~f[\frac{2}{3}]\\ ~F[\frac{1}{3}] \end{matrix}\right\}, \cdots,~ \left\{\begin{matrix} \vdots \\ c^2[\frac{20}{10}]\\ c^1[\frac{10}{10}] \end{matrix}\right\}\subset \left\{\begin{matrix} \vdots \\ ~ ~~c^1[\frac{20}{10}]\\ ces^2[\frac{19}{10}]\\ bes^1[\frac{18}{10}]\\ ~ ~~a^1[\frac{17}{10}]\\ ~as^1[\frac{16}{10}]\\ ~ ~~g^1[\frac{15}{10}]\\ ges^1[\frac{14}{10}]\\ ~ ~~f^1[\frac{13}{10}]\\ ~es^1[\frac{12}{10}]\\ des^1[\frac{11}{10}]\\ ~ ~~c^1[\frac{10}{10}]\\ ~bes[\frac{9}{10}]\\ ~~as[\frac{8}{10}]\\ ~ges[\frac{7}{10}]\\ ~~es[\frac{6}{10}]\\ ~~ ~~c[\frac{5}{10}]\\ ~As[\frac{4}{10}]\\ Es_1[\frac{3}{10}]\\ As_1[\frac{2}{10}]\\ As_2[\frac{1}{10}] \end{matrix}\right\}, \cdots

\begin{align} & 1 = 1 & (m = 0)\\[10pt] & \boldsymbol{a}\cdot \boldsymbol{x} = a_1 x_1 + a_2 x_2 + a_3 x_3 & (m = 1)\\[10pt] & \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y}\\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} \end{vmatrix} \\[4pt] = {} & \begin{vmatrix} a_2 & a_3\\ b_2 & b_3 \end{vmatrix} \begin{vmatrix} x_2 & y_2\\ x_3 & y_3 \end{vmatrix} + \begin{vmatrix} a_3 & a_1\\ b_3 & b_1 \end{vmatrix} \begin{vmatrix} x_3 & y_3\\ x_1 & y_1 \end{vmatrix} + \begin{vmatrix} a_1 & a_2\\ b_1 & b_2 \end{vmatrix} \begin{vmatrix} x_1 & y_1\\ x_2 & y_2 \end{vmatrix}\\[4pt] = {} & (\boldsymbol{a}\times\boldsymbol{b})\cdot(\boldsymbol{x}\times\boldsymbol{y}) & (m = 2)\\[10pt] & \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y} & \boldsymbol{a}\cdot \boldsymbol{z}\\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} & \boldsymbol{b}\cdot \boldsymbol{z}\\ \boldsymbol{c}\cdot \boldsymbol{x} & \boldsymbol{c}\cdot \boldsymbol{y} & \boldsymbol{c}\cdot \boldsymbol{z} \end{vmatrix} = \begin{vmatrix} a_1 & a_2 & a_3\\ b_1 & b_2 & b_3\\ c_1 & c_2 & c_3 \end{vmatrix} \begin{vmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{vmatrix}\\[4pt] = {} & [\boldsymbol{a}\cdot (\boldsymbol{b} \times \boldsymbol{c})] [\boldsymbol{x}\cdot (\boldsymbol{y} \times \boldsymbol{z})] & (m = 3)\\[10pt] & \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y} & \boldsymbol{a}\cdot \boldsymbol{z} & \boldsymbol{a}\cdot \boldsymbol{w} \\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} & \boldsymbol{b}\cdot \boldsymbol{z} & \boldsymbol{b}\cdot \boldsymbol{w} \\ \boldsymbol{c}\cdot \boldsymbol{x} & \boldsymbol{c}\cdot \boldsymbol{y} & \boldsymbol{c}\cdot \boldsymbol{z} & \boldsymbol{c}\cdot \boldsymbol{w} \\ \boldsymbol{d}\cdot \boldsymbol{x} & \boldsymbol{d}\cdot \boldsymbol{y} & \boldsymbol{d}\cdot \boldsymbol{z} & \boldsymbol{d}\cdot \boldsymbol{w} \end{vmatrix} = 0 & (m = 4) \end{align}

\begin{vmatrix} i \setminus & R_0 & \gg & s_a & R_1\\ 1 & 0 & 1 & 1 & 1 \\ 2 & 0 & 0 & 0 & 0 \\ 3 & 0 & 0 & 0 & 0 \\ 4 & 0 & 0 & 1 & 0 \\ 5 & 0 & 0 & 0 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_b & R_2\\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_c & R_3 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_a & R_4 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_b & R_5 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_c & R_6 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_a & R_7 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \end{vmatrix} \begin{vmatrix} \gg & s_c & R_8 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \end{vmatrix}

\begin{align} 1 &= 1 & (m = 0)\\ \boldsymbol{a}\cdot \boldsymbol{x} &= a_1 x_1 + a_2 x_2 + a_3 x_3 & (m = 1)\\ \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y}\\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} \end{vmatrix} &= \begin{vmatrix} a_2 & a_3\\ b_2 & b_3 \end{vmatrix} \begin{vmatrix} x_2 & y_2\\ x_3 & y_3 \end{vmatrix} + \begin{vmatrix} a_3 & a_1\\ b_3 & b_1 \end{vmatrix} \begin{vmatrix} x_3 & y_3\\ x_1 & y_1 \end{vmatrix} + \begin{vmatrix} a_1 & a_2\\ b_1 & b_2 \end{vmatrix} \begin{vmatrix} x_1 & y_1\\ x_2 & y_2 \end{vmatrix}\\ &= (\boldsymbol{a}\times\boldsymbol{b})\cdot(\boldsymbol{x}\times\boldsymbol{y}) & (m = 2)\\ \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y} & \boldsymbol{a}\cdot \boldsymbol{z}\\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} & \boldsymbol{b}\cdot \boldsymbol{z}\\ \boldsymbol{c}\cdot \boldsymbol{x} & \boldsymbol{c}\cdot \boldsymbol{y} & \boldsymbol{c}\cdot \boldsymbol{z} \end{vmatrix} &= \begin{vmatrix} a_1 & a_2 & a_3\\ b_1 & b_2 & b_3\\ c_1 & c_2 & c_3 \end{vmatrix} \begin{vmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{vmatrix}\\ &= [\boldsymbol{a}\cdot (\boldsymbol{b} \times \boldsymbol{c})] [\boldsymbol{x}\cdot (\boldsymbol{y} \times \boldsymbol{z})] & (m = 3)\\ \begin{vmatrix} \boldsymbol{a}\cdot \boldsymbol{x} & \boldsymbol{a}\cdot \boldsymbol{y} & \boldsymbol{a}\cdot \boldsymbol{z} & \boldsymbol{a}\cdot \boldsymbol{w} \\ \boldsymbol{b}\cdot \boldsymbol{x} & \boldsymbol{b}\cdot \boldsymbol{y} & \boldsymbol{b}\cdot \boldsymbol{z} & \boldsymbol{b}\cdot \boldsymbol{w} \\ \boldsymbol{c}\cdot \boldsymbol{x} & \boldsymbol{c}\cdot \boldsymbol{y} & \boldsymbol{c}\cdot \boldsymbol{z} & \boldsymbol{c}\cdot \boldsymbol{w} \\ \boldsymbol{d}\cdot \boldsymbol{x} & \boldsymbol{d}\cdot \boldsymbol{y} & \boldsymbol{d}\cdot \boldsymbol{z} & \boldsymbol{d}\cdot \boldsymbol{w} \end{vmatrix} &= 0 & (m = 4) \end{align}

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  • 22130 \mapsto A \mapsto B
  • 21614 \big \big\|
  • 21228 \sim A \sim B
  • 21106 \cfrac \cfrac B C
  • 21018 \oplus A \oplus B
  • 20233 \rightleftharpoons A \rightleftharpoons B
  • 20066 \mathit \mathit B
  • 19698 \neg A \neg B
  • 19166 \uparrow A \uparrow B
  • 19164 \Lambda \Lambda
  • 19145 \ne A \ne B
  • 19062 \vert \vert
  • 18196 \Big \Big\|
  • 17856 \exists \exists
  • 16431 \underbrace \underbrace B
  • 16197 \Theta \Theta
  • 15534 \textbf \textbf B
  • 15315 \land A \land B
  • 14693 \Leftrightarrow A \Leftrightarrow B
  • 13810 \ddot \ddot B
  • 13705 \widehat \widehat B
  • 13561 \N \N
  • 13228 \pmod A \pmod B
  • 12377 \textrm \textrm B
  • 12325 \setminus A \setminus B
  • 12234 \bigg \bigg\|
  • 12090 \det \det
  • 11978 \leqslant A \leqslant B
  • 11775 \Pi \Pi
  • 11642 \vartheta \vartheta
  • 11571 \Z \Z
  • 11512 \max \max B
  • 11491 \bullet \bullet
  • 10944 \lor A \lor B
  • 10867 \lfloor A \lfloor B
  • 10829 \and A \and B
  • 10725 \part \part
  • 10550 \downarrow A \downarrow B
  • 10388 \rfloor A \rfloor B
  • 10346 \cosh \cosh B
  • 10344 \binom \binom B C
  • 10212 \overset \overset{=} B
  • 10143 \sinh \sinh B

= < 10,000 =

  • 9730 \vee A \vee B
  • 9643 \arctan \arctan B
  • 9568 \cot \cot B
  • 9545 \not \not B
  • 9309 \star A \star B
  • 9196 \dagger \dagger
  • 9194 \oint \oint B
  • 9128 \ddots A \ddots B
  • 9084 \vdash A \vdash B
  • 8968 \simeq A \simeq B
  • 8559 \lnot A \lnot B
  • 8340 \underset \underset B C
  • 8181 \aleph \aleph
  • 8166 \min \min B
  • 8151 \emptyset \emptyset
  • 8125 \bigcup A \bigcup B
  • 7992 \stackrel \stackrel B C
  • 7650 \angle A \angle B
  • 7418 \cong A \cong B
  • 7208 \triangle A \triangle B
  • 7196 \ast A \ast B
  • 7145 \varnothing \varnothing
  • 7051 \sup A \sup B
  • 6874 \leftrightarrow A \leftrightarrow B
  • 6849 \Bigg \Bigg\|
  • 6795 \rang A \rang B
  • 6555 \sec \sec B
  • 6369 \C \C
  • 6320 \perp A \perp B
  • 6243 \bmod A \bmod B
  • 6198 \or A \or B
  • 6167 \top A \top B
  • 6128 \lbrace A \lbrace B
  • 6049 \geqslant A \geqslant B
  • 5966 \varrho A \varrho B
  • 5940 \Pr A \Pr B
  • 5916 \rbrace A \rbrace B
  • 5796 \Vert A \Vert B
  • 5748 \texttt \texttt B
  • 5682 \ce \ce{B}
  • 5558 \leftarrow A \leftarrow B
  • 5512 \iff A \iff B
  • 5328 \hbox \hbox{B}
  • 5317 \mod A \mod B
  • 5264 \iint \iint B
  • 5217 \Box A \Box B
  • 5143 \bigl \bigl( B \bigr)
  • 5085 \bigr
  • 4889 \notin A \notin B
  • 4876 \arcsin \arcsin B
  • 4842 \hline \begin{array}{c} A \\ \hline B\end{array}
  • 4734 \propto A \propto B
  • 4665 \arccos \arccos B
  • 4608 \supset A \supset B
  • 4556 \odot A \odot B
  • 4369 \acute \acute B
  • 4352 \implies A \implies B
  • 4197 \csc \csc B
  • 4128 \mathop \mathop B
  • 4121 \dotsc A \dotsc B
  • 4117 \tanh \tanh B
  • 4084 \ll A \ll B
  • 4080 \iota \iota
  • 4079 \dim A \dim B
  • 4018 \lbrack A \lbrack B
  • 3976 \rbrack A \rbrack B
  • 3811 \bigcap A \bigcap B
  • 3801 \inf A \inf B
  • 3749 \rceil A \rceil B
  • 3720 \textit \textit B
  • 3649 \Q \Q
  • 3477 \bot A \bot B
  • 3473 \atop A \atop B
  • 3402 \varkappa \varkappa
  • 3322 \parallel A \parallel B
  • 3309 \div A \div B
  • 3259 \lceil A \lceil B
  • 3259 \Bbb A \Bbb B
  • 3203 \Bigl \Bigl( B \Bigr)
  • 3137 \backslash \backslash
  • 3096 \# A\#B
  • 3039 \Bigr
  • 3022 \Re \Re B
  • 2988 \mp A \mp B
  • 2948 \% A\%B
  • 2916 \infin A \infin B
  • 2851 \exist \exist
  • 2808 \ker A \ker B
  • 2752 \cancel \cancel B
  • 2738 \sgn \sgn B
  • 2731 \upsilon \upsilon
  • 2725 \overbrace A \overbrace B
  • 2723 \models A \models B
  • 2665 \arg A \arg B
  • 2646 \iiint A \iiint B
  • 2592 \tbinom \tbinom B C
  • 2546 \therefore A \therefore B
  • 2452 \dotsb A \dotsb B
  • 2447 \gg A \gg B
  • 2388 \widetilde A \widetilde B
  • 2281 \biggl \biggl( B \biggr)
  • 2265 \deg A \deg B
  • 2263 \lg A \lg B
  • 2234 \square A \square B
  • 2204 \Longrightarrow A \Longrightarrow B
  • 2163 \rarr A \rarr B
  • 2153 \biggr
  • 2016 \flat A \flat B
  • 2012 \Beta \Beta
  • 2010 \cal \cal B
  • 2006 \limsup A \limsup B
  • 1933 \lVert A \lVert B
  • 1893 \bigoplus A \bigoplus B
  • 1855 \Longleftrightarrow A \Longleftrightarrow B
  • 1841 \backprime A \backprime B
  • 1834 \rVert A \rVert B
  • 1828 \Alpha \Alpha
  • 1706 \sen A \sen B
  • 1702 \bf \bf B
  • 1672 \Xi \Xi
  • 1654 \lang A \lang B
  • 1584 \rightleftarrows A \rightleftarrows B
  • 1567 \gcd A \gcd B
  • 1551 \Downarrow A \Downarrow B
  • 1530 \bigwedge A \bigwedge B
  • 1527 \hookrightarrow A \hookrightarrow B
  • 1522 \centerdot A \centerdot B
  • 1500 \wp A \wp B
  • 1496 \sharp A \sharp B
  • 1495 \supseteq A \supseteq B
  • 1479 \succ A \succ B
  • 1442 \imath A \imath B
  • 1438 \ominus A \ominus B
  • 1420 \liminf A \liminf B
  • 1408 \isin A \isin B
  • 1393 \Diamond A \Diamond B
  • 1367 \_ A\_B
  • 1354 \empty A \empty B
  • 1326 \searrow A \searrow B
  • 1326 \Im A \Im B
  • 1293 \subsetneq A \subsetneq B
  • 1272 \coth A \coth B
  • 1255 \nearrow A \nearrow B
  • 1217 \blacksquare A \blacksquare B
  • 1206 \gets A \gets B
  • 1204 \bigodot A \bigodot B
  • 1191 \varsigma \varsigma
  • 1165 \arccot \arccot B
  • 1160 \ni A \ni B
  • 1148 \Leftarrow A \Leftarrow B
  • 1138 \longmapsto A \longmapsto B
  • 1126 \it \it B
  • 1080 \longleftarrow A \longleftarrow B
  • 1080 \lesssim A \lesssim B
  • 1074 \nolimits \operatorname{A} \nolimits B
  • 1053 \triangleleft A \triangleleft B
  • 1046 \leqq A \leqq B
  • 1032 \check \check B
  • 1030 \arcsec \arcsec B
  • 1023 \prec A \prec B
  • 1003 \varpi \varpi

= < 1000 =

  • 999 \prec A \prec B
  • 976 \backprime A^\backprime
  • 964 \beth \beth
  • 954 \Upsilon \Upsilon
  • 945 \varpi \varpi
  • 943 \Tau \Tau
  • 923 \vDash A \vDash B
  • 922 \sqcup A \sqcup B
  • 916 \Eta \Eta
  • 907 \sdot A \sdot B
  • 898 \vartriangle A \vartriangle B
  • 877 \preceq A \preceq B
  • 875 \diagup A \diagup B
  • 873 \Chi \Chi
  • 857 \triangledown A \triangledown B
  • 853 \mathtt \mathtt B
  • 820 \ddagger \ddagger
  • 810 \bigvee \bigvee
  • 794 \scriptscriptstyle A \scriptscriptstyle B
  • 793 \Epsilon \Epsilon
  • 784 \Vdash A \Vdash B
  • 771 \doteq A \doteq B
  • 770 \bigtriangleup A \bigtriangleup B
  • 760 \surd A \surd B
  • 746 \geqq A \geqq B
  • 744 \boxplus A \boxplus B
  • 737 \sqsubseteq A \sqsubseteq B
  • 737 \$ A\$B
  • 735 \sub A \sub B
  • 730 \arccsc \arccsc B
  • 725 \longleftarrow A \longleftarrow B
  • 722 \triangleright A \triangleright B
  • 706 \twoheadrightarrow A \twoheadrightarrow B
  • 704 \And \And
  • 702 \pagecolor {\pagecolor{Cyan} B}
  • 692 \rtimes A \rtimes B
  • 675 \complement \complement
  • 674 \clubsuit \clubsuit
  • 673 \Kappa \Kappa
  • 654 \nmid A \nmid B
  • 643 \textsf \textsf B
  • 641 \triangleq A \triangleq B
  • 634 \Iota \Iota
  • 630 \coprod A \coprod B
  • 624 \Biggl \Biggl\|
  • 618 \diamond \diamond
  • 602 \smile \smile
  • 601 \biguplus A \biguplus B
  • 594 \H \H
  • 590 \& A\&B
  • 587 \grave \grave B
  • 570 \Zeta \Zeta
  • 565 \breve A \breve B
  • 559 \hom A \hom B
  • 555 \jmath A \jmath B
  • 547 \thicksim A \thicksim B
  • 547 \Biggr \Biggr\|
  • 545 \Mu \Mu
  • 544 \frown \frown
  • 539 \Uparrow A \Uparrow B
  • 539 \Rho \Rho
  • 535 \mathord A \mathord B
  • 533 \measuredangle A \measuredangle B
  • 530 \swarrow A \swarrow B
  • 528 \longleftrightarrow A \longleftrightarrow B
  • 527 \rightsquigarrow A \rightsquigarrow B
  • 525 \succeq A \succeq B
  • 520 \dotsm A \dotsm B
  • 518 \cancelto A \cancelto B C
  • 516 \sphericalangle A \sphericalangle B
  • 507 \bigcirc A \bigcirc B
  • 490 \grp unknown function
  • 489 \spadesuit \spadesuit
  • 487 \lll A \lll B
  • 485 \bigstar A \bigstar B
  • 482 \heartsuit A \heartsuit B
  • 470 \smallsetminus A \smallsetminus B
  • 441 \updownarrow A \updownarrow B
  • 437 \bigotimes A \bigotimes B
  • 428 \Nu \Nu
  • 422 \diamondsuit \diamondsuit
  • 417 \mathrel A \mathrel B C
  • 413 \nwarrow A \nwarrow B
  • 407 \leftrightarrows A \leftrightarrows B
  • 402 \leftrightharpoons A \leftrightharpoons B
  • 397 \overleftarrow A \overleftarrow B
  • 396 \uplus A \uplus B
  • 392 \gtrsim A \gtrsim B
  • 388 \circledast A \circledast B
  • 386 \natural \natural
  • 380 \preccurlyeq A \preccurlyeq B
  • 373 \Omicron \Omicron
  • 372 \boxdot A \boxdot B
  • 370 \bigsqcup A \bigsqcup B
  • 369 \because A \because B
  • 367 \dotso A \dotso B
  • 362 \Updownarrow A \Updownarrow B
  • 361 \succsim A \succsim B
  • 350 \sqcap A \sqcap B
  • 349 \wr A \wr B
  • 348 \plusmn A \plusmn B
  • 344 \euro A \euro B
  • 337 \bigtriangledown A \bigtriangledown B
  • 334 \succcurlyeq A \succcurlyeq B
  • 334 \�
  • 331 \xleftarrow A \xleftarrow B
  • 324 \dashv A \dashv B
  • 324 \AA A \AA B
  • 320 \omicron \omicron
  • 317 \ar unknown function
  • 313 \nexists A \nexists B
  • 313 \digamma A \digamma B
  • 305 \trianglelefteq A \trianglelefteq B
  • 304 \upharpoonright A \upharpoonright B
  • 303 \dbinom \dbinom B C
  • 295 \rightharpoonup A \rightharpoonup B
  • 294 \urcorner A \urcorner B
  • 291 \vartriangleleft A \vartriangleleft B
  • 287 \boxtimes A \boxtimes B
  • 284 \diagdown A \diagdown B
  • 278 \ulcorner A \ulcorner B
  • 278 \mho \mho
  • 277 \ltimes A \ltimes B
  • 277 \definecolor \definecolor{myorange}{rgb}{1,0.65,0.4}\color{myorange}orange
  • 267 \rightrightarrows A \rightrightarrows B
  • 265 \Rrightarrow A \Rrightarrow B
  • 263 \mathbin A \mathbin B
  • 263 \ggg A \ggg B
  • 257 \varinjlim A \varinjlim B
  • 256 \blacktriangleright A \blacktriangleright B
  • 253 \veebar A \veebar B
  • 245 \hslash \hslash
  • 244 \oslash \oslash
  • 243 \varpropto A \varpropto B
  • 243 \varprojlim A \varprojlim B
  • 241 \S \S
  • 237 \thickapprox A \thickapprox B
  • 231 \sideset \sideset{_1^2}{_3^4}\prod
  • 231 \Game A \Game B
  • 230 \vline A \vline B
  • 230 \intercal \intercal
  • 229 \sube A \sube B
  • 229 \gimel \gimel
  • 227 \nrightarrow A \nrightarrow B
  • 227 \lrcorner A \lrcorner B
  • 225 \mathopen A \mathopen B
  • 224 \Longleftarrow A \Longleftarrow B
  • 222 \nsubseteq A \nsubseteq B
  • 221 \sqsubset A \sqsubset B
  • 221 \multimap A \multimap B
  • 217 \iiiint \iiiint B
  • 216 \precsim A \precsim B
  • 212 \bowtie A \bowtie B
  • 211 \nleftarrow A \nleftarrow B
  • 209 \lessdot A \lessdot B
  • 206 \gtrdot A \gtrdot B
  • 206 \fallingdotseq A \fallingdotseq B
  • 204 \pitchfork A \pitchfork B
  • 147 \/
  • 110 \"
  • 92 \[
  • 88 \:
  • 57 \]
  • 57 \.
  • 41 \<
  • 25 \1
  • 22 \>
  • 20 \?
  • 16 \=
  • 15 \(
  • 13 \3
  • 13 \)
  • 13 \'
  • 11 \-
  • 10 \2
  • 9 \0
  • 9 \*
  • 8 \^
  • 6 \5
  • 6 \~
  • 2 \9
  • 2 \`
  • 1 \6
  • 1 \+

100 - 199

  • 199 \circledcirc A \circledcirc B
  • 198 \blacktriangle A \blacktriangle B
  • 197 \ang A \ang B
  • 194 \curlywedge A \curlywedge B
  • 194 \blacktriangledown A \blacktriangledown B
  • 187 \backsim A \backsim B
  • 184 \eth \eth
  • 182 \checkmark A \checkmark B
  • 178 \real \real
  • 176 \rightarrowtail A \rightarrowtail B
  • 176 \lessapprox A \lessapprox B
  • 176 \approxeq A \approxeq B
  • 175 \daleth A \daleth B
  • 175 \curvearrowright A \curvearrowright B
  • 174 \rightharpoondown A \rightharpoondown B
  • 174 \reals \reals
  • 173 \nparallel A \nparallel B
  • 171 \vartriangleright A \vartriangleright B
  • 171 \nleftrightarrow A \nleftrightarrow B
  • 169 \varlimsup A \varlimsup B
  • 167 \circlearrowleft A \circlearrowleft B
  • 167 \alef \alef
  • 166 \circlearrowright A \circlearrowright B
  • 165 \overleftrightarrow A \overleftrightarrow B
  • 165 \hookleftarrow A \hookleftarrow B
  • 164 \boxminus A \boxminus B
  • 162 \supsetneq A \supsetneq B
  • 161 \subsetneqq A \subsetneqq B
  • 159 \nRightarrow A \nRightarrow B
  • 158 \asymp A \asymp B
  • 156 \eqslantless A \eqslantless B
  • 154 \varsubsetneq A \varsubsetneq B
  • 154 \mathclose A \mathclose B
  • 154 \gtrless A \gtrless B
  • 151 \lessgtr A \lessgtr B
  • 151 \Bbbk A \Bbbk B
  • 150 \dotplus A \dotplus B
  • 148 \nvDash A \nvDash B
  • 148 \curlyvee A \curlyvee B
  • 147 \P A \P B
  • 146 \llcorner A \llcorner B
  • 145 \amalg A \amalg B
  • 144 \bcancel A \bcancel B
  • 139 \Dagger A \Dagger B
  • 138 \upharpoonleft A \upharpoonleft B
  • 138 \leftharpoondown A \leftharpoondown B
  • 137 \backepsilon A \backepsilon B
  • 136 \sqsupseteq A \sqsupseteq B
  • 136 \doteqdot A \doteqdot B
  • 135 \curvearrowleft A \curvearrowleft B
  • 134 \sqsupset A \sqsupset B
  • 133 \shortparallel A \shortparallel B
  • 132 \downharpoonright A \downharpoonright B
  • 131 \nvdash A \nvdash B
  • 131 \nLeftrightarrow A \nLeftrightarrow B
  • 129 \leftharpoonup A \leftharpoonup B
  • 128 \gtrapprox A \gtrapprox B
  • 128 \downharpoonleft A \downharpoonleft B
  • 126 \backsimeq A \backsimeq B
  • 125 \xcancel A \xcancel B
  • 125 \leftrightsquigarrow A \leftrightsquigarrow B
  • 124 \smallsmile A \smallsmile B
  • 121 \nsim A \nsim B
  • 121 \blacklozenge A \blacklozenge B
  • 120 \risingdotseq A \risingdotseq B
  • 120 \Finv A \Finv B
  • 119 \upuparrows A \upuparrows B
  • 119 \Subset A \Subset B
  • 119 \O A \O B
  • 118 \nLeftarrow A \nLeftarrow B
  • 118 \blacktriangleleft A \blacktriangleleft B
  • 117 \Lsh A \Lsh B
  • 117 \doublebarwedge A \doublebarwedge B
  • 116 \subseteqq A \subseteqq B
  • 116 \lesseqqgtr A \lesseqqgtr B
  • 115 \lozenge A \lozenge B
  • 115 \gtreqqless A \gtreqqless B
  • 115 \Cup A \Cup B
  • 115 \barwedge A \barwedge B
  • 113 \shortmid A \shortmid B
  • 112 \eqno unknown function
  • 111 \Rarr A \Rarr B
  • 111 \bull A \bull B
  • 110 \restriction A \restriction B
  • 110 \ngtr A \ngtr B
  • 109 \nolimits \operatorname{A}\nolimits B
  • 109 \divideontimes A \divideontimes B
  • 108 \nVdash A \nVdash B
  • 108 \lneq A \lneq B
  • 108 \eqslantgtr A \eqslantgtr B
  • 107 \varsupsetneq A \varsupsetneq B
  • 107 \nsupseteq A \nsupseteq B
  • 107 \npreceq A \npreceq B
  • 107 \ncong A \ncong B
  • 107 \leftleftarrows A \leftleftarrows B
  • 107 \gtreqless A \gtreqless B
  • 106 \emph Undefined control sequence
  • 105 \nleqslant A \nleqslant B
  • 105 \lneqq A \lneqq B
  • 105 \gneq A \gneq B
  • 105 \circledS \circledS
  • 104 \varsubsetneqq A \varsubsetneqq B
  • 104 \ngeqslant A \ngeqslant B
  • 104 \looparrowright A \looparrowright B
  • 103 \varliminf A \varliminf B
  • 103 \downdownarrows A \downdownarrows B
  • 102 \Lleftarrow A \Lleftarrow B
  • 102 \curlyeqprec A \curlyeqprec B
  • 101 \supsetneqq A \supsetneqq B
  • 101 \succapprox A \succapprox B
  • 101 \precapprox A \precapprox B
  • 101 \nsucceq A \nsucceq B
  • 101 \lesseqgtr A \lesseqgtr B
  • 101 \gneqq A \gneqq B
  • 101 \curlyeqsucc A \curlyeqsucc B
  • 101 \circleddash A \circleddash B
  • 101 \Cap A \Cap B
  • 100 \succnsim A \succnsim B
  • 100 \precnsim A \precnsim B
  • 100 \nprec A \nprec B
  • 100 \leftarrowtail A \leftarrowtail B
  • 100 \gvertneqq A \gvertneqq B
  • 100 \bumpeq A \bumpeq B
  • 100 \between A \between B

10 - 99

  • 99 \varsupsetneqq A \varsupsetneqq B
  • 99 \ntriangleleft A \ntriangleleft B
  • 99 \nsucc A \nsucc B
  • 99 \nsubseteqq A \nsubseteqq B
  • 99 \nleqq A \nleqq B
  • 99 \lvertneqq A \lvertneqq B
  • 99 \lnapprox A \lnapprox B
  • 98 \Supset A \Supset B
  • 98 \succnapprox A \succnapprox B
  • 98 \Rsh A \Rsh B
  • 98 \precnapprox A \precnapprox B
  • 98 \ngeqq A \ngeqq B
  • 98 \looparrowleft A \looparrowleft B
  • 98 \lnsim A \lnsim B
  • 98 \gnapprox A \gnapprox B
  • 98 \eqcirc A \eqcirc B
  • 97 \Vvdash A \Vvdash B
  • 97 \rightthreetimes A \rightthreetimes B
  • 97 \nshortmid A \nshortmid B
  • 97 \eqsim A \eqsim B
  • 96 \nVDash A \nVDash B
  • 96 \ntrianglerighteq A \ntrianglerighteq B
  • 96 \gnsim A \gnsim B
  • 96 \Bumpeq A \Bumpeq B
  • 95 \supseteqq A \supseteqq B
  • 95 \precneqq A \precneqq B
  • 95 \ntrianglelefteq A \ntrianglelefteq B
  • 95 \leftthreetimes A \leftthreetimes B
  • 94 \succneqq A \succneqq B
  • 94 \ntriangleright A \ntriangleright B
  • 94 \nsupseteqq A \nsupseteqq B
  • 94 \nshortparallel A \nshortparallel B
  • 94 \circeq A \circeq B
  • 76 \dotsi A \dotsi B
  • 74 \harr A \harr B
  • 69 \rArr A \rArr B
  • 65 \Stigma A \Stigma B
  • 65 \Sampi A \Sampi B
  • 65 \Coppa A \Coppa B
  • 63 \nleq A \nleq B
  • 63 \Koppa A \Koppa B
  • 59 \oiint A \oiint B
  • 56 \varcoppa A \varcoppa B
  • 55 \varstigma A \varstigma B
  • 55 \twoheadleftarrow A \twoheadleftarrow B
  • 53 \nless A \nless B
  • 50 \Complex A \Complex B
  • 49 \lrarr A \lrarr B
  • 45 \trianglerighteq A \trianglerighteq B
  • 44 \larr A \larr B
  • 43 \darr A \darr B
  • 42 \textvisiblespace A \textvisiblespace B
  • 36 \stigma A \stigma B
  • 31 \smallfrown A \smallfrown B
  • 26 \ngeq A \ngeq B
  • 26 \Digamma A \Digamma B
  • 25 \hArr A \hArr B
  • 23 \image A \image B
  • 21 \uarr A \uarr B
  • 20 \koppa A \koppa B
  • 19 \mathpunct A \mathpunct B
  • 17 \sampi A \sampi B
  • 15 \supe A \supe B
  • 15 \Larr A \Larr B
  • 15 \coppa A \coppa B
  • 14 \oiiint A \oiiint B
  • 14 \Harr A \Harr B
  • 12 \gggtr A \gggtr B
  • 11 \weierp A \weierp B
  • 11 \thetasym A \thetasym B
  • 11 \doublecup A \doublecup B
  • 11 \doublecap A \doublecap B
  • 10 \projlim A \projlim B
  • 10 \Doteq A \Doteq B

Unknown function

  • 59 \vep
  • 39 \bR
  • 38 \be
  • 35 \label
  • 35 \del
  • 31 \textup
  • 30 \bC
  • 28 \phii
  • 27 \circle
  • 26 \middle
  • 24 \rule
  • 24 \put
  • 24 \cL
  • 23 \bibitem
  • 22 \cite
  • 21 \quadr
  • 21 \phantom
  • 21 \fbox
  • 20 \tag
  • 20 \buildrel
  • 18 \unitlength
  • 18 \textsl
  • 17 \TeX
  • 17 \set
  • 16 \cline
  • 16 \chigre
  • 15 \wti
  • 15 \comen
  • 14 \vardelta
  • 14 \subsection
  • 14 \lt
  • 13 \final
  • 12 \xybox
  • 12 \xlongrightarrow
  • 12 \setlength
  • 12 \newpage
  • 12 \multicolumn
  • 12 \Db
  • 12 \ag
  • 11 \fra
  • 11 \Cl
  • 10 \w
  • 10 \vv
  • 10 \leadsto
  • 10 \from
  • 10 \enskip
  • 10 \dddot
  • 10 \bzdrh

2 - 9

  • 8 \officialeuro A \officialeuro B
  • 8 \injlim A \injlim B
  • 7 \geneuronarrow A \geneuronarrow B
  • 7 \alefsym \alefsym
  • 6 \geneurowide \geneurowide
  • 6 \geneuro \geneuro
  • 7 \Reals \Reals
  • 7 \hearts \hearts
  • 5 \diamonds \diamonds
  • 4 \spades \spades
  • 4 \clubs \clubs
  • 2 \ointctrclockwise A \ointctrclockwise B
  • 3 \varointclockwise A \varointclockwise B

All others fail

  • 9 \tt ,
  • 9 \setf ,
  • 9 \ryl ,
  • 9 \pmb ,
  • 9 \Ob ,
  • 9 \near ,
  • 9 \h ,
  • 9 \f ,
  • 9 \def ,
  • 9 \chemical ,
  • 9 \buyer ,
  • 8 \section ,
  • 8 \Rset ,
  • 8 \parcial ,
  • 8 \lefteqn ,
  • 8 \ldotp ,
  • 8 \ket ,
  • 8 \hphantom ,
  • 8 \gt ,
  • 8 \g ,
  • 8 \borel ,
  • 7 \vcenter ,
  • 7 \U ,
  • 7 \sijoitus ,
  • 7 \Mb ,
  • 7 \LaTeX ,
  • 7 \hfill ,
  • 7 \cU ,
  • 6 \valor ,
  • 6 \triple ,
  • 6 \textasciimacron ,
  • 6 \subsubsection ,
  • 6 \permil ,
  • 6 \par ,
  • 6 \obg ,
  • 6 \maya ,
  • 6 \mathc ,
  • 6 \math ,
  • 6 \m ,
  • 6 \ensin ,
  • 6 \COS ,
  • 6 \cfra ,
  • 6 \caption ,
  • 6 \bzdrv ,
  • 5 \vp ,
  • 5 \unknownname ,
  • 5 \Un ,
  • 5 \prueba ,
  • 5 \PD ,
  • 5 \ober ,
  • 5 \nab ,
  • 5 \large ,
  • 5 \kern ,
  • 5 \Kb ,
  • 5 \K ,
  • 5 \hspace ,
  • 5 \fraction ,
  • 5 \Ef ,
  • 5 \correcte ,
  • 5 \anfty ,
  • 4 \xlog ,
  • 4 \usepackage ,
  • 4 \upgamma ,
  • 4 \Textbf ,
  • 4 \substack ,
  • 4 \setin ,
  • 4 \scriptsize ,
  • 4 \ref ,
  • 4 \Paris ,
  • 4 \ov ,
  • 4 \operator ,
  • 4 \o ,
  • 4 \nT ,
  • 4 \nNum ,
  • 4 \nISBN ,
  • 4 \nEditora ,
  • 4 \nAutor ,
  • 4 \M ,
  • 4 \limdir ,
  • 4 \LARGE ,
  • 4 \Ha ,
  • 4 \greek ,
  • 4 \fr ,
  • 4 \fly ,
  • 4 \dto ,
  • 4 \deixat ,
  • 4 \co ,
  • 4 \cdotd ,
  • 4 \bgcolor ,
  • 4 \B ,
  • 3 \xrightleftharpoons ,
  • 3 \wref ,
  • 3 \widering ,
  • 3 \wideparen ,
  • 3 \underrightarrow ,
  • 3 \sun ,
  • 3 \sumI ,
  • 3 \stopchemical ,
  • 3 \startchemical ,
  • 3 \spirituslenis ,
  • 3 \space ,
  • 3 \SL ,
  • 3 \setcounter ,
  • 3 \sech ,
  • 3 \rto ,
  • 3 \pdiff ,
  • 3 \pcoef ,
  • 3 \overrigntarrow ,
  • 3 \overarc ,
  • 3 \nonumber ,
  • 3 \naphdrh ,
  • 3 \Montreal ,
  • 3 \mathring ,
  • 3 \lyl ,
  • 3 \link ,
  • 3 \lin ,
  • 3 \Lb ,
  • 3 \Large ,
  • 3 \j ,
  • 3 \inter ,
  • 3 \infinity ,
  • 3 \im ,
  • 3 \idotsint ,
  • 3 \i ,
  • 3 \Huge ,
  • 3 \Hom ,
  • 3 \formel ,
  • 3 \fD ,
  • 3 \etc ,
  • 3 \Esp ,
  • 3 \displayed ,
  • 3 \dag ,
  • 3 \csch ,
  • 3 \cr ,
  • 3 \cotg ,
  • 3 \cosec ,
  • 3 \conv ,
  • 3 \cdotp ,
  • 3 \bra ,
  • 3 \bF ,
  • 3 \Bell ,
  • 3 \barphi ,
  • 3 \atan ,
  • 3 \al ,
  • 2 \y ,
  • 2 \xt ,
  • 2 \xrightharpoonup ,
  • 2 \xrightharpoondown ,
  • 2 \xleftrightharpoons ,
  • 2 \xleftharpoonup ,
  • 2 \xleftharpoondown ,
  • 2 \X ,
  • 2 \widetriangle ,
  • 2 \widecheck ,
  • 2 \widebar ,
  • 2 \widearrow ,
  • 2 \vet ,
  • 2 \verb ,
  • 2 \V ,
  • 2 \utilde ,
  • 2 \ushortw ,
  • 2 \ushortdw ,
  • 2 \ushort ,
  • 2 \uprho ,
  • 2 \upmu ,
  • 2 \upalpha ,
  • 2 \unrhd ,
  • 2 \unlhd ,
  • 2 \unichar ,
  • 2 \underleftrightarrow ,
  • 2 \underleftarrow ,
  • 2 \undergroup ,
  • 2 \underbracket ,
  • 2 \textwon ,
  • 2 \textnaira ,
  • 2 \textlira ,
  • 2 \texteuro ,
  • 2 \textdong ,
  • 2 \textbackslash ,
  • 2 \textasciicircum ,
  • 2 \te ,
  • 2 \suma ,
  • 2 \strokedint ,
  • 2 \sp ,
  • 2 \sout ,
  • 2 \Sn ,
  • 2 \smallint ,
  • 2 \sigmaeA ,
  • 2 \rrbracket ,
  • 2 \rO ,
  • 2 \rn ,
  • 2 \ri ,
  • 2 \rhd ,
  • 2 \require ,
  • 2 \Relbar ,
  • 2 \relbar ,
  • 2 \ra ,
  • 2 \queq ,
  • 2 \punts ,
  • 2 \pir ,
  • 2 \pecat ,
  • 2 \partialvartrcirclerightint ,
  • 2 \partialvartrcircleleftint ,
  • 2 \partialvartlcirclerightint ,
  • 2 \partialvartlcircleleftint ,
  • 2 \partialvardrcirclerightint ,
  • 2 \partialvardrcircleleftint ,
  • 2 \partialvardlcirclerightint ,
  • 2 \partialvardlcircleleftint ,
  • 2 \p ,
  • 2 \ovsetl ,
  • 2 \overgroup ,
  • 2 \overbracket ,
  • 2 \orc ,
  • 2 \OMega ,
  • 2 \ob ,
  • 2 \normalcolor ,
  • 2 \nonsubset ,
  • 2 \naturals ,
  • 2 \natnums ,
  • 2 \meq ,
  • 2 \mathe ,
  • 2 \mapstochar ,
  • 2 \Map ,
  • 2 \Lra ,
  • 2 \llbracket ,
  • 2 \Lille ,
  • 2 \lhd ,
  • 2 \leftguillemets ,
  • 2 \Ld ,
  • 2 \Laplace ,
  • 2 \laplace ,
  • 2 \lange ,
  • 2 \Join ,
  • 2 \inv ,
  • 2 \input ,
  • 2 \IM ,
  • 2 \Homework ,
  • 2 \hole ,
  • 2 \gset ,
  • 2 \grdot ,
  • 2 \frak ,
  • 2 \for ,
  • 2 \footnote ,
  • 2 \foo ,
  • 2 \fint ,
  • 2 \fatsemi ,
  • 2 \en ,
  • 2 \eiquipas ,
  • 2 \effb ,
  • 2 \double ,
  • 2 \dl ,
  • 2 \dft ,
  • 2 \dashrightarrow ,
  • 2 \cls ,
  • 2 \cdotn ,
  • 2 \boxed ,
  • 2 \bE ,
  • 2 \Bar ,
  • 2 \baliseTEX ,
  • 2 \atl ,
  • 2 \alt ,
  • 2 \Abgp ,
  • 2 \aa ,

= 1 =

  • 1 \Lrarr {\displaystyle A\Lrarr B} translated to \Leftrightarrow
  • 1 \lrArr {\displaystyle A\lrArr B} \Leftrightarrow
  • 1 \lArr {\displaystyle A\lArr B} \Leftarrow
  • 1 \Darr {\displaystyle A\Darr B} \Downarrow
  • 1 \dArr {\displaystyle A\dArr B} \Downarrow
  • 1 \Uarr {\displaystyle A\Uarr B} \Uparrow
  • 1 \uArr {\displaystyle A\uArr B} \Uparrow
  • 1 \cnums {\displaystyle \cnums} \mathbb {C}
  • 1 \sect {\displaystyle \sect } \S

Other give syntax errors

\addcontentsline

\adots

\alad

\alas

\alatpha

\alfa

\allset

\alphaup

\amp

\angstrom

\angud

\angus

\antilabe

\any

\apprge

\apprle

\approxcolon

\approxcoloncolon

\arcosh

\arcoth

\arcsch

\arcsen

\arrownot

\arrowvert

\arsech

\arsinh

\artanh

\atomic

\author

\autoleftarrow

\autoleftrightharpoons

\autorightarrow

\autorightleftharpoons

\backapprox

\backapproxeq

\backcong

\backeqsim

\backneg

\backslashdiv

\backtriplesim

\barin

\barleftharpoon

\baro

\barrightharpoon

\bbslash

\betaup

\bigbox

\bigboxasterisk

\bigboxbackslash

\bigboxbot

\bigboxcirc

\bigboxcoasterisk

\bigboxdiv

\bigboxdot

\bigboxleft

\bigboxminus

\bigboxplus

\bigboxright

\bigboxslash

\bigboxtimes

\bigboxtop

\bigboxtriangleup

\bigboxvoid

\bigcapdot

\bigcapplus

\bigcircle

\bigcomplementop

\bigcupdot

\bigcupplus

\bigcurlyvee

\bigcurlyveedot

\bigcurlywedge

\bigcurlywedgedot

\bigdoublecurlyvee

\bigdoublecurlywedge

\bigdoublevee

\bigdoublewedge

\bigint

\biginterleave

\bignplus

\bigoast

\bigoasterisk

\bigobackslash

\bigobot

\bigocirc

\bigocoasterisk

\bigodiv

\bigoleft

\bigominus

\bigoright

\bigoslash

\bigostar

\bigotop

\bigotriangle

\bigotriangleup

\bigovert

\bigovoid

\bigparallel

\bigparr

\bigplus

\bigsqcap

\bigsqcapdot

\bigsqcapplus

\bigsqcupdot

\bigsqcupplus

\bigsquplus

\bigtimes

\bigvarstar

\bigveedot

\bigwedgedot

\bigwee

\bigwith

\binampersand

\bindnasrepma

\blackdiamond

\blacktriangleup

\blitza

\blitzb

\blitzc

\blitzd

\blitze

\block

\botdoteq

\box

\boxast

\boxasterisk

\boxbackslash

\boxbar

\boxbot

\boxbox

\boxbslash

\boxcirc

\boxcircle

\boxcoasterisk

\boxdiv

\boxdotleft

\boxdotLeft

\boxdotright

\boxdotRight

\boxempty

\boxleft

\boxLeft

\boxright

\boxRight

\boxslash

\boxtop

\boxtriangleup

\boxvert

\boxvoid

\bracevert

\bran

\bumpedeq

\bZ

\capdot

\capplus

\cdotP

\cdotZ

\chemarrow

\chiup

\circledbar

\circledbslash

\circleddotleft

\circleddotright

\circledgtr

\circledless

\circledR

\circledvee

\circledwedge

\circleleft

\circleright

\circplus

\cj

\closedcurlyvee

\closedcurlywedge

\closedequal

\closedprec

\closedsucc

\cnums

\coasterisk

\coAsterisk

\coh

\colonapprox

\coloncolon

\coloncolonapprox

\coloncolonequals

\coloncolonminus

\coloncolonsim

\coloneq

\coloneqq

\colonequals

\colonminus

\colonsim

\colour

\con

\conjunctive

\const

\convolution

\corresponds

\cotan

\cronometra

\crux

\cshuffle

\cupdot

\cupplus

\curlyveedot

\curlyveedownarrow

\curlyveeuparrow

\curlywedgedot

\curlywedgedownarrow

\curlywedgeuparrow

\cursive

\curvearrowbotleft

\curvearrowbotleftright

\curvearrowbotright

\curvearrowdownup

\curvearrowleftright

\curvearrownesw

\curvearrownwse

\curvearrowrightleft

\curvearrowsenw

\curvearrowswne

\curvearrowupdown

\dArr

\dasheddownarrow

\dashedleftarrow

\dashednearrow

\dashednwarrow

\dashedrightarrow

\dashedsearrow

\dashedswarrow

\dasheduparrow

\dashleftarrow

\dashleftrightarrow

\dashVv

\dblcolon

\dd

\ddddot

\dddtstile

\ddotdot

\ddotsy

\ddststile

\ddtstile

\ddttstile

\degree

\deltaup

\dex

\dfourier

\diagram

\diameter

\diamondbackslash

\diamonddiamond

\diamonddot

\diamonddots

\diamondminus

\diamondplus

\diamondslash

\diamondtimes

\diamondvert

\dina

\directs

\divdot

\divides

\dlsh

\dn

\dndtstile

\dnststile

\dntstile

\dnttstile

\documentclass

\dotarrow

\dotdiv

\dotmedvert

\dotminus

\dotseq

\dotsint

\dottimes

\doublecurlyvee

\doublecurlywedge

\doublefrown

\doublefrowneq

\doublesmile

\doublesmileeq

\doublesqcap

\doublesqcup

\doublevee

\doublewedge

\downarrowtail

\downdownharpoons

\downfilledspoon

\downfootline

\downfree

\downharpoonccw

\downharpooncw

\downlsquigarrow

\downmapsto

\downmodels

\downModels

\downpitchfork

\downpropto

\downrsquigarrow

\downslice

\downspoon

\downtherefore

\downtouparrow

\downuparrows

\downupharpoons

\downvdash

\downVdash

\downY

\drsh

\dsdtstile

\dsststile

\dststile

\dsttstile

\dtdtstile

\dtimes

\dtststile

\dttstile

\dtttstile

\eipsilon

\emptysetz

\enddiagram

\epsilonup

\eqbump

\eqbumped

\eqcolon

\eqdot

\eqfrown

\eqqcolon

\eqsmile

\equal

\equalclosed

\equalscolon

\equalscoloncolon

\equivclosed

\esquerre

\et

\etaup

\evensidemargin

\fatbslash

\fatslash

\ffff

\fgeA

\fgebackslash

\fgebaracute

\fgebarcap

\fgec

\fgecap

\fgecapbar

\fgecup

\fgecupacute

\fgecupbar

\fged

\fgee

\fgeeszett

\fgeeta

\fgef

\fgeF

\fgeinfty

\fgelangle

\fgelb

\fgeleftB

\fgeleftC

\fgeN

\fgeoverU

\fgerightarrow

\fgerightB

\fges

\fgestruckone

\fgestruckzero

\fgeU

\fgeuparrow

\fgeupbracket

\filleddiamond

\filledmedsquare

\filledmedtriangledown

\filledmedtriangleleft

\filledmedtriangleright

\filledmedtriangleup

\filledsquare

\filledstar

\filledtriangledown

\filledtriangleleft

\filledtriangleright

\filledtriangleup

\fivedots

\fixedddots

\fixedvdots

\floor

\flqq

\footnotesize

\fourier

\fourth

\frathbf

\fratto

\frowneq

\frowneqsmile

\frownsmile

\frownsmileeq

\frqq

\gammaup

\geqclosed

\geqdot

\geqslantdot

\ggcurly

\glqq

\grqq

\gsdg

\gtr

\gtrclosed

\gtreqlessslant

\gtrneqqless

\gue

\hAar

\hash

\hateq

\hbipropto

\hcrossing

\hdotdot

\hdots

\he

\hexamethylenei

\holter

\href

\ht

\htmladdnormallink

\huge

\iddots

\if

\incoh

\infinite

\inG

\inplus

\intbar

\intclockwise

\interleave

\intI

\intop

\inty

\invamp

\invbackneg

\invneg

\iotaup

\jm

\joinrel

\kali

\kappaup

\ksi

\l

\lambdabar

\lambdaslash

\lambdaup

\lamdba

\landdownint

\landupint

\lAngle

\langlebar

\langlej

\largetriangledown

\largetriangleleft

\largetriangleright

\largetriangleup

\lArr

\larrowfill

\latex

\lbag

\lBrack

\lCeil

\lcirclearrowdown

\lcirclearrowleft

\lcirclearrowright

\lcirclearrowup

\lcircleleftint

\lcirclerightint

\lcorners

\lcurvearrowdown

\lcurvearrowleft

\lcurvearrowne

\lcurvearrownw

\lcurvearrowright

\lcurvearrowse

\lcurvearrowsw

\lcurvearrowup

\ldbrack

\leftarrowtriangle

\leftbarharpoon

\leftevaw

\leftfilledspoon

\leftfootline

\leftfree

\lefthalfcap

\lefthalfcup

\leftharpoonccw

\leftharpooncw

\leftleftharpoons

\leftlsquigarrow

\leftmapsto

\leftmodels

\leftModels

\leftpitchfork

\leftpropto

\leftrightarroweq

\leftrightarrowtriangle

\leftrightharpoon

\leftrightharpoondownup

\leftrightharpoonsfill

\leftrightharpoonupdown

\leftrightline

\leftrsquigarrow

\leftslice

\leftspoon

\leftsquigarrow

\lefttherefore

\lefttorightarrow

\leftvdash

\leftVdash

\leftwave

\leftX

\lem

\leqc

\leqclosed

\leqdot

\leqslantdot

\leslant

\less

\lessclosed

\lesseqgtrslant

\lessneqqgtr

\letf

\levaw

\lfilet

\lFloor

\lgroup

\lgx

\lhook

\lhookdownarrow

\lhookleftarrow

\lhooknearrow

\lhooknwarrow

\lhookrightarrow

\lhooksearrow

\lhookswarrow

\lhookuparrow

\lightning

\listoffigures

\lJoin

\llangle

\llceil

\llcurly

\llfloor

\llless

\llparenthesis

\lmoustache

\logof

\longarrow

\longmapsfrom

\looparrowdownleft

\looparrowdownright

\lower

\lrArr

\lrtimes

\lsem

\ltriple

\lvert

\lwave

\lwavy

\lWavy

\maketitle

\maldekstra

\maltese

\mappedfromchar

\mapsfrom

\mapsfromchar

\masterdir

\mat

\matbf

\mathaccent

\mathbbA

\mathca

\mathcent

\mathdollar

\mathellipsis

\mathnormal

\mathparagraph

\mathrd

\mathrn

\mathscr

\mathsection

\mathsterling

\mathunderscore

\matriu

\matrix

\matrm

\md

\medbackslash

\medbullet

\medcirc

\medcircle

\meddiamond

\medslash

\medsquare

\medstar

\medtriangledown

\medtriangleleft

\medtriangleright

\medtriangleup

\medvert

\medvertdot

\merge

\mi

\midy

\minus

\minuscolon

\minuscoloncolon

\minusdot

\minuso

\mmappedfromchar

\mmapstochar

\moo

\mS

\multimapboth

\multimapbothvert

\multimapdot

\multimapdotboth

\multimapdotbothA

\multimapdotbothAvert

\multimapdotbothB

\multimapdotbothBvert

\multimapdotbothvert

\multimapdotinv

\multimapinv

\muup

\mvert

\mVert

\napprox

\napproxeq

\nasymp

\nbackapprox

\nbackapproxeq

\nbackcong

\nbackeqsim

\nbacksim

\nbacksimeq

\nbacktriplesim

\nBeachte

\nbeschreibt

\nbumpeq

\nBumpeq

\ncirceq

\ncirclearrowleft

\ncirclearrowright

\nclosedequal

\ncurlyeqprec

\ncurlyeqsucc

\ncurvearrowdownup

\ncurvearrowleft

\ncurvearrowleftright

\ncurvearrownesw

\ncurvearrownwse

\ncurvearrowright

\ncurvearrowrightleft

\ncurvearrowsenw

\ncurvearrowswne

\ncurvearrowupdown

\ndasharrow

\ndasheddownarrow

\ndashedleftarrow

\ndashednearrow

\ndashednwarrow

\ndashedrightarrow

\ndashedsearrow

\ndashedswarrow

\ndasheduparrow

\ndashleftarrow

\ndashrightarrow

\ndashv

\ndashV

\nDashv

\nDashV

\ndashVv

\nddtstile

\nDer

\ndiagdown

\ndiagup

\ndivides

\ndoteq

\nDoteq

\ndoublefrown

\ndoublefrowneq

\ndoublesmile

\ndoublesmileeq

\ndownarrow

\nDownarrow

\ndownarrowtail

\ndowndownarrows

\ndownfilledspoon

\ndownfootline

\ndownfree

\ndownharpoonccw

\ndownharpooncw

\ndownlsquigarrow

\ndownmapsto

\ndownmodels

\ndownModels

\ndownpitchfork

\ndownrsquigarrow

\ndownspoon

\ndownuparrows

\ndownupharpoons

\ndownvdash

\ndownVdash

\ndres

\ndststile

\ndtstile

\ndttstile

\nearrowtail

\nearrowy

\nefilledspoon

\nefootline

\nefree

\neharpoonccw

\neharpooncw

\nelsquigarrow

\nemapsto

\nemodels

\neModels

\nenearrows

\nepitchfork

\neqbump

\neqcirc

\neqdot

\neqfrown

\neqsim

\neqslantgtr

\neqslantless

\neqsmile

\nequal

\nequalclosed

\nequiv

\nequivclosed

\nersquigarrow

\nespoon

\neswarrow

\neswarrows

\neswbipropto

\neswcrossing

\neswharpoonnwse

\neswharpoons

\neswharpoonsenw

\neswline

\nevdash

\neVdash

\newextarrow

\nfallingdotseq

\nfrown

\nfrowneq

\nfrowneqsmile

\nfrownsmile

\nfrownsmileeq

\ngeqclosed

\ngeqdot

\ngeqslantdot

\ngets

\ngg

\nggg

\ngtrapprox

\ngtrclosed

\ngtrdot

\ngtreqless

\ngtreqlessslant

\ngtreqqless

\ngtrless

\ngtrsim

\nhateq

\nhookleftarrow

\nhookrightarrow

\nin

\niplus

\niv

\nlcirclearrowdown

\nlcirclearrowleft

\nlcirclearrowright

\nlcirclearrowup

\nlcurvearrowdown

\nlcurvearrowleft

\nlcurvearrowne

\nlcurvearrownw

\nlcurvearrowright

\nlcurvearrowse

\nlcurvearrowsw

\nlcurvearrowup

\nleadsto

\nleftarrowtail

\nleftfilledspoon

\nleftfootline

\nleftfree

\nleftharpoonccw

\nleftharpooncw

\nleftleftarrows

\nleftlsquigarrow

\nleftmapsto

\nleftmodels

\nleftModels

\nleftpitchfork

\nleftrightarrows

\nleftrightharpoondownup

\nleftrightharpoons

\nleftrightharpoonupdown

\nleftrightline

\nLeftrightline

\nleftrightsquigarrow

\nleftrsquigarrow

\nleftspoon

\nleftvdash

\nleftVdash

\nleqclosed

\nleqdot

\nleqslantdot

\nlessapprox

\nlessclosed

\nlessdot

\nlesseqgtr

\nlesseqgtrslant

\nlesseqqgtr

\nlessgtr

\nlesssim

\nlhookdownarrow

\nlhookleftarrow

\nlhooknearrow

\nlhooknwarrow

\nlhookrightarrow

\nlhooksearrow

\nlhookswarrow

\nlhookuparrow

\nll

\nLleftarrow

\nlll

\nmapsto

\nMit

\nmodels

\nndtstile

\nnearrow

\nNearrow

\nnearrowtail

\nnefilledspoon

\nnefootline

\nnefree

\nneharpoonccw

\nneharpooncw

\nnelsquigarrow

\nnemapsto

\nnemodels

\nneModels

\nnenearrows

\nnepitchfork

\nnersquigarrow

\nnespoon

\nneswarrow

\nNeswarrow

\nneswarrows

\nneswharpoonnwse

\nneswharpoons

\nneswharpoonsenw

\nneswline

\nNeswline

\nnevdash

\nneVdash

\nnststile

\nntstile

\nnttstile

\nnwarrow

\nNwarrow

\nnwarrowtail

\nnwfilledspoon

\nnwfootline

\nnwfree

\nnwharpoonccw

\nnwharpooncw

\nnwlsquigarrow

\nnwmapsto

\nnwmodels

\nnwModels

\nnwnwarrows

\nnwpitchfork

\nnwrsquigarrow

\nnwsearrow

\nNwsearrow

\nnwsearrows

\nnwseharpoonnesw

\nnwseharpoons

\nnwseharpoonswne

\nnwseline

\nNwseline

\nnwspoon

\nnwvdash

\nnwVdash

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Pages with problematic Latex syntax

See User:Texvc2LaTeXBot.

Total pages 1229

  • 544 (Article)
  • 210 Talk
  • 246 User
  • 55 User talk
  • 145 Wikipedia
  • 17 Wikipedia talk
  • 1 Draft
  • 2 File talk
  • 1 Help
  • 2 Help talk
  • 2 MediaWiki talk
  • 4 Template

class = "wikitable"

! page

AndOrBoldPartBbbAngCHDollarPercent
Absorption (logic)94--------
Addition--1-------
Advection--7-------
Affine focal set--30-------
Affine geometry1---------
Affine group------1---
Airway resistance--1-------
Ak singularity--1-------
Albrecht v. Herald Co.---5------
Analytical Society---1------
Andreotti–Frankel theorem--2-------
Andreotti–Norguet formula2---------
Andrzej Grzegorczyk12--------
Angle notation-----2----
Angular Correlation of Electron Positron Annihilation Radiation--9-------
Angular velocity--25-------
Annuity--------2-
Antisymmetric relation3---------
Appert topology--1-------
Appleton–Hartree equation--3-------
Arbitrage betting--------2-
Argument (complex analysis)1---------
Arithmetic Fuchsian group------3---
Arithmetic function1---------
Arithmetic group------3---
Arithmetical hierarchy2-1-------
Array processing--9-------
Associative property33--------
Augmented Lagrangian method--3-------
Automobile drag coefficient--1-------
Axiom of adjunction-1--------
Axiom of infinity43--------
Axiom of limitation of size5---------
Axiom of pairing13--------
Axiom of union1---------
Axiom schema of replacement1---------
Axiom schema of specification5---------
BCK algebra1---------
BPST instanton--1-------
Balanced set------1---
Banach–Alaoglu theorem------1---
Bapat–Beg theorem1---------
Barrier function--3-------
Bas van Fraassen1---------
Belinfante–Rosenfeld stress–energy tensor--2-------
Beltrami identity---10------
Bennett acceptance ratio---2------
Beta distribution---20------
Biconditional introduction1---------
Binary Goppa code1---------
Binary number-1--------
Bingham plastic--13-------
Bivector22--------
Blancmange curve--1-------
Bloch equations--7-------
Bloch wave – MoM method--10-------
Bochner–Martinelli formula2---------
Bolometric correction---------2
Boole's expansion theorem---1------
Born–von Karman boundary condition--3-------
Bézout matrix------2---
CR manifold------41---
CTL*33--------
CW--1-------
CW complex------2---
Cahn–Hilliard equation--2-------
Calculus of variations---13------
Canonical basis--9-------
Canonical quantization--5-------
Capillary wave--1-------
Carrier frequency offset-----1----
Carry operator-1--------
Cartan formalism (physics)--1-------
Castigliano's method--3-------
Catch-22 (logic)-1--------
Cauchy problem---1------
Cayley transform--2-------
Center-of-momentum frame--15-------
Central composite design--3-------
Characterization of probability distributions--7-------
Charge density--25-------
Chern–Simons form--6-------
Church encoding1---------
Church's thesis (constructive mathematics)--2-------
Circular surface--1-------
Citroën--1-------
Clarence Irving Lewis1---------
Class logic1---------
Classical field theory--1-------
Closest point method--3-------
Clustering coefficient-1--------
Cobordism------2---
Coefficients of potential---1------
Combustion instability--3-------
Commutative property22--------
Commutativity of conjunction14---------
Complex number-----1----
Compound interest--------1-
Computation tree logic21--------
Computational Fluid Dynamics for Phase Change Materials--1-------
Conditioned disjunction21--------
Cone (topology)--1-------
Conflict-Driven Clause Learning-4--------
Conjunction fallacy2---------
Conjunction introduction4---------
Conjunctive normal form79--------
Connection (mathematics)--5-------
Consequentia mirabilis-1--------
Conservation form--5-------
Conservation law--2-------
Consistency-1--------
Consistent histories-1--------
Constraint (mathematics)--5-------
Constructible universe21--------
Construction of the real numbers61--------
Constructive dilemma17--------
Continuous geometry-1--------
Continuum hypothesis-1--------
Contraposition52--------
Convergent matrix--11-------
Cook–Levin theorem1---------
Cotangent bundle1---------
Coupling (physics)--2-------
Covariant derivative--3-------
Covariant formulation of classical electromagnetism--16-------
Critical point (mathematics)--2-------
Crowds1---------
Cubic function---------1
Cubic harmonic--11-------
Current density--6-------
Currying11--------
Czesław Lejewski11--------
De Broglie–Bohm theory--3-------
De Morgan's laws76--------
Debye–Hückel equation---3------
Deductive lambda calculus1---------
Definite description1---------
Del---2------
Deposition (geology)------1---
Derivative---3------
Deriving the Schwarzschild solution---2------
Destructive dilemma29--------
Diffeomorphism---1------
Differential equation---1------
Diffraction--12-------
Dilution ratio---------2
Dirac algebra--2-------
Directional derivative--20-------
Dirichlet-multinomial distribution--3-------
Discrete valuation------1---
Discursive dilemma1---------
Disjunction elimination15--------
Disjunction introduction-5--------
Disjunctive normal form55--------
Disjunctive syllogism13--------
Dispersion (water waves)--1-------
Dissipative operator--1-------
Distributive lattice-1--------
Distributive property67--------
Divisor topology--1-------
Donkey sentence3---------
Dot product--2---1---
Double origin topology--2-------
Draft:DaríoBL--2-------
Dual representation------2---
Duality (mathematics)--1-------
Dupin cyclide------1---
E6 (mathematics)--4-------
Eigendecomposition of a matrix------1---
Eigenvalue algorithm--11------
Eisenbud–Levine–Khimshiashvili signature formula--3-------
Ekman layer---2------
Electric dipole moment--36-------
Electric potential energy--1-------
Electro Thermal Dynamic Stripping Process---2------
Electromagnetic stress–energy tensor--5-------
Electromagnetic tensor--2-------
Elementary class1---------
Elliptic orbit--1-------
Elliptic partial differential equation---1------
Ellis drainhole--3-------
Empty lattice approximation--15-------
Energy operator--1-------
Engine--2-------
Ensemble averaging (machine learning)--2-------
Enthalpy---2------
Entropy (classical thermodynamics)---4------
Envelope (mathematics)--4-------
Euclidean quantum gravity--4-------
Euler angles--4-------
Euler equations (fluid dynamics)--64-------
Evasive Boolean function32--------
Evenly spaced integer topology--1-------
Exchangeable random variables--9-------
Exclusive or31--------
Existential quantification-1--------
Exponential map (Lie theory)--2-------
Exportation (logic)12---------
Exterior algebra--1-------
External ray------5---
Fatou's theorem------2---
Field extension------5---
File talk:Noncont.svg1---------
File talk:Propositional logic.png11--------
First class constraint--3-------
First quantization--7-------
Fixed-point combinator4---------
Flat morphism------6---
Flux balance analysis--4-------
Focus recovery based on the linear canonical transform--2-------
Ford–Fulkerson algorithm---------1
Formula--4-------
Fourier optics--3-------
Fractional calculus---1------
Freivalds' algorithm2---------
Frequency selective surface--11-------
Friedel oscillations--2-------
Frobenius reciprocity------1---
Froude number--4-------
Fréchet algebra------3---
Frölicher–Nijenhuis bracket1---------
Functional derivative---1------
Fundamental increment lemma--2-------
Fundamental theorem of Galois theory------2---
Fuzzy subalgebra1-2-------
Fürer's algorithm---------1
GPOPS-II--9-------
Galilean transformation--3-------
Gauge theory--8-------
Gauss's law for gravity---3------
Gaussian integral--1-------
Gauss–Codazzi equations--6-------
General number field sieve--1-------
General set theory-2--------
Generalized eigenvector--71-------
Geometric algebra1---------
Gibbs–Duhem equation--11-------
Glossary of fuel cell terms--1-------
Golomb ruler2---------
Grad–Shafranov equation--14-------
Gramian matrix--1-------
Green's identities--2-------
Guide number---------1
Hamiltonian (quantum mechanics)--211------
Hamilton–Jacobi equation--8-------
Heat capacity ratio---1------
Heat equation--3-------
Heaviside condition---------5
Help talk:Displaying a formula--1-------
Help talk:Displaying a formula/Archive 2--4-------
Help:Displaying a formula11-------1
Hemocytometer---------1
Hessenberg variety------1---
Hessian matrix--5-------
Heyting algebra54--------
Hirzebruch signature theorem------2---
History monoid--4-------
History of logic22--------
Hopf fibration--5-------
Hyperfunction------8---
Hypothetical syllogism1---------
Indiscernibles22--------
Inductive probability266--------
Infinitary logic7---------
Information dimension-------19--
Information source (mathematics)--2-------
Inner measure---------4
Instanton--5-------
Integral domain------6---
Intensity (physics)--1-------
Interest--------4-
Interlocking interval topology--1-------
Intermediate logic1---------
Intertemporal CAPM--3-------
Inverse distance weighting---1------
Inversion (discrete mathematics)3---------
Inversive congruential generator------1---
Isotope dilution1---------
Kadir–Brady saliency detector---1------
Karel Lambert3---------
Kepler orbit--28-------
Kissing number problem2---------
Klein–Gordon equation--2-------
Kolmogorov–Arnold representation theorem--3-------
Kolmogorov–Smirnov test2---------
Koopmans' theorem--2-------
Kripke–Platek set theory32--------
Krippendorff's alpha---------1
LSZ reduction formula---15------
Lalande 21185---------2
Lambda calculus definition21--------
Lambda lifting1546--------
Lattice Boltzmann methods---10------
Law of demand--3-------
Laws of Form12--------
Leading and lagging current-----4----
Leonhard Euler--1-------
Let expression221--------
Lift (data mining)4---------
Light field microscopy--24-------
Line element--6-------
Linear independence--2-------
Linear programming1---------
Linearization--6-------
List of common physics notations---2------
List of equations in classical mechanics--15-------
List of equations in fluid mechanics--1-------
List of first-order theories6---------
List of mathematical symbols1---------
Logical NOR13--------
Logical biconditional74--------
Logical conjunction312--------
Logical connective11--------
Logical disjunction-8--------
Lojban grammar-5--------
Lorentz force---1------
MODFLOW--3-------
Maass wave form-------27--
Machine olfaction---3------
Macroscopic quantum phenomena---3------
Madelung equations--7-------
Magic hypercube---------1
Magnetic dipole–dipole interaction--4-------
Magnetic moment--5-------
Magnetic resonance (quantum mechanics)--50-------
Magnetic susceptibility---1------
Manifold------2---
Mass flow rate--6-------
Mass flux--13-------
Material conditional33--------
Material implication (rule of inference)16--------
Material nonimplication1---------
Mathematical descriptions of the electromagnetic field--27-------
Mathematical formulation of the Standard Model--24-------
Matrix addition--3-------
Matrix calculus--1-------
Matrix splitting--15-------
Max-flow min-cut theorem-2--------
Maxwell's equations--1-------
MediaWiki talk:Common.css/Archive 9---------2
MediaWiki talk:Monobook.css---------2
Mega-Merger41--------
Mereology111--------
Mereotopology42--------
Metamaterial--2-------
Method of analytic tableaux21--------
Minimum message length3---------
Mixing length model---4------
Modal fallacy11--------
Modal logic4---------
Modal matrix--8-------
Mode 7--7-------
Modus ponendo tollens1---------
Modus tollens21--------
Moment of inertia--1-------
Momentum operator--9-------
Morphism of schemes------1---
Morse–Kelley set theory72--------
Muller automaton1---------
Multi-index notation---5------
Multi-task learning1-3-------
Multidimensional network--1-------
Multinomial distribution--2-------
Multiphase particle-in-cell method--17-------
Multivariate kernel density estimation--25-------
Möbius energy--22-------
Möbius plane------6---
NAND gate3---------
Narrowing of algebraic value sets643--------
Nearly free electron model--49-------
Necessity and sufficiency2---------
Negation43--------
Negation as failure33--------
Negation introduction1---------
Newton–Euler equations--4-------
Nijenhuis–Richardson bracket1---------
Non-covalent interactions index--2-------
Non-uniform rational B-spline--4-------
Null set1---------
Oblivious ram1---------
Operator (physics)--22-------
Optical theorem--2-------
Option type1---------
Optional stopping theorem1---------
Orbit--18-------
Orbit portrait------1---
Orbital stability------2---
Ordered field1---------
Ordered pair22--------
Ordinal utility2---------
Orientation (vector space)--2-------
PSPACE-complete22--------
Pair production--3-------
Paraconsistent logic1---------
Parallel (geometry)1---------
Parseval–Gutzmer formula------1---
Partial differential equation---5------
Partition function (mathematics)--2-------
Pauli equation--1-------
Peirce's law11--------
Penalty method--5-------
Perifocal coordinate system--10-------
Perturbation theory--1-------
Phase angle-----1----
Pilot wave theory--1-------
Pitchfork bifurcation---2------
Pitman shorthand11--------
Plane (geometry)--17-------
Poisson's equation--3-------
Polar sine--4-------
Polarization of an algebraic form--3-------
Polyadic space1---------
Polytope------1---
Pontryagin duality------1---
Population balance equation--1-------
Position (vector)--7-------
Position and momentum space--1-------
Position operator--3-------
Post canonical system--------1-
Potential energy--3-------
Power (physics)--4-------
Predicate functor logic52--------
Preference (economics)2---------
Preon star4---------
Principle of explosion1---------
Product rule--3-------
Projection-valued measure--1-------
Proof by contradiction-1--------
Propagator--1-------
Propositional calculus23--------
Propositional proof system--1-------
Proxima Centauri---------1
Proxima Centauri b---------1
Pumping lemma for context-free languages1---------
Pumping lemma for regular languages11--------
Q0 (mathematical logic)1-1-------
Quadrature based moment methods--17-------
Quadrupole--1-------
Quantifier (logic)11--------
Quantum digital signature1---------
Quantum finite automata--1-------
Quantum potential1---------
Quater-imaginary base------2---
Quaternionic manifold-------14--
Quotient of a formal language11--------
Rabi cycle--2-------
Radial distribution function--1-------
Randolph diagram-1--------
Rashba effect--6-------
Rational number11--------
Rayleigh dissipation function--1-------
Real element-1--------
Reduced mass--6-------
Reflections of signals on conducting lines---------4
Relational algebra-1--------
Relaxation (NMR)--3-------
Representation of a Lie group------1---
Representation theory of finite groups------87---
Representation theory of the Lorentz group------114---
Reproducing kernel Hilbert space------1---
Riemann zeta function------1---
Root of unity modulo n--1-------
Rotation group SO(3)--16-------
Rotational partition function--1-------
Rotordynamics--1-------
Rough set67--------
Rules of passage (logic)33--------
S (set theory)1---------
SHA-22---------
SLD resolution15--------
Second derivative---3------
Second quantization--24-------
Selection (relational algebra)31--------
Sequent calculus2231--------
Serial relation2---------
Set-builder notation1---------
Sheffer stroke21--------
Shock capturing method--2-------
Singular homology--5-------
Situation calculus1---------
Sobol sequence--4-------
Soler model------1---
Spark (mathematics)--5-------
Spectral flux density--12-------
Spectral sequence--2-------
Spence's function------1---
Sphaleron--2-------
Spin representation------1---
Spinors in three dimensions--2-------
Spline (mathematics)--8-------
Split-step method---6------
Standard Boolean model21--------
Stiff equation--19---2---
Streamline diffusion--7-------
Structural acoustics--1-------
Submodular set function--9-------
Substitution tiling--13-------
Superlattice---2------
Supermembranes--3-------
Superparamagnetic relaxometry--1-------
Supervenience1---------
Surface layer---3------
Syllogism4---------
Symmetric function--1-------
System of linear equations--13-------
Tarski's axioms153--------
Tautology (logic)-1--------
Tautology (rule of inference)66--------
Template:Bigmath/doc---2------
Template:NumBlk/doc--36-------
Template:Oiint/doc--8-------
Template:Oiint/sandbox--5-------
Temporal logic12--------
Tetrad formalism--5-------
The General Theory of Employment, Interest and Money---1------
Thermoacoustics---1------
Third derivative--1-------
Third law of thermodynamics---3------
Three subgroups lemma--2-------
Tight binding--3-------
Topological K-theory------1---
Torus knot------6---
Total variation diminishing---2------
Totally positive matrix--4-------
Transposition (logic)-2--------
Two-electron atom--2-------
Two-port network---------4
Type (model theory)11--------
Uncertainty theory11--------
Unique homomorphic extension theorem11--------
Uniquely inversible grammar1---------
Universal geometric algebra-1--------
Universal quantification1---------
Valuation ring------8---
Variety (universal algebra)--5-------
Vector calculus--6-------
Vector clock1---------
Vector model of the atom--6-------
Vector-valued function--1-------
Versor (physics)--5-------
Volkswagen Lupo--1-------
Von Neumann–Bernays–Gödel set theory362--------
Voronoi diagram2---------
Vorticity confinement--1-------
Vuong's closeness test--3-------
Wave equation--24------
Wave packet--10-------
Weierstrass–Enneper parameterization--1-------
Weingarten equations--4-------
Weyl–Brauer matrices--5-------
Wheeler–DeWitt equation--2-------
Whitehead's point-free geometry71--------
Whitney extension theorem--2-------
Witten zeta function-1--------
Yao's principle--4-------
Zero-suppressed decision diagram11--------
Talk:0.999.../Archive 24---------
Talk:0.999.../Arguments/Archive 42---------
Talk:Abductive reasoning11--------
Talk:Abel–Ruffini theorem------1---
Talk:African Americans/Archive 7---------12
Talk:Aleph number6---------
Talk:Algebraic notation (chess)11--------
Talk:Almost complex manifold---3------
Talk:Amity---------1
Talk:Anaheim Hills, Anaheim, California/archive 1---------3
Talk:Antisymmetric relation2---------
Talk:Approximation error---------1
Talk:Atan23---------
Talk:Atheism/Archive 341---------
Talk:Atheism/Archive 351---------
Talk:Axiom of choice/Archive 21---------
Talk:Axiom of choice/Archive 31---------
Talk:Axiom of choice/Archive 53---------
Talk:Axiom of infinity13--------
Talk:Axiom of limitation of size4---------
Talk:Axiom of pairing11--------
Talk:Axiom of union43--------
Talk:Axiom schema of replacement2---------
Talk:Axiom schema of specification1---------
Talk:Banach–Tarski paradox1---------
Talk:Bent function-1--------
Talk:Beta distribution---2------
Talk:Binary Goppa code2---------
Talk:Birefringence---9------
Talk:Boolean algebra (structure)/Archive 1-1--------
Talk:Boolean algebra/Archive 488--------
Talk:Bra–ket notation/Archive 1--2-------
Talk:Burusera--------1-
Talk:Calculus/Archive 3-1--------
Talk:Cardinal number11-------1
Talk:Cauchy problem---1------
Talk:Centrifugal force/Archive 17--5-------
Talk:Church's thesis (constructive mathematics)--1-------
Talk:Clustering coefficient11--------
Talk:Collatz conjecture/Archive 2---------1
Talk:Complex affine space------3---
Talk:Confusion of the inverse---------9
Talk:Conjugacy class1---------
Talk:Construction of the real numbers71--------
Talk:Continuity equation--4-------
Talk:Continuity equation/Archive 1--5-------
Talk:Continuum hypothesis11--------
Talk:Counting quantification1---------
Talk:Creation–evolution controversy/Archive 5---------1
Talk:Curry's paradox21--------
Talk:Definable real number3---------
Talk:Definite description2---------
Talk:Derivative---2------
Talk:Diffie–Hellman key exchange/Archive 1---------2
Talk:Distributive property11--------
Talk:Divergence theorem/Archive 1---1------
Talk:Divisor1---------
Talk:Double layer (plasma physics)--1-------
Talk:Drinker paradox-1--------
Talk:Electric current/Archive 21---------
Talk:Ellsberg paradox--------7-
Talk:Entropy/Archive 111---------
Talk:Equations of motion--6-------
Talk:Euclidean division11--------
Talk:Euclidean quantum gravity--3-------
Talk:Euler angles/Archive 1--1-------
Talk:Euler equations (fluid dynamics)--6-------
Talk:Exportation (logic)24--------
Talk:Fictitious force/Archive 2--1-------
Talk:Finite set1---------
Talk:Fixed-point combinator1---------
Talk:Flux/Archive 1--2-------
Talk:Forces on sails/sandbox--1-------
Talk:Four-vector--2-------
Talk:Friedel oscillations--1-------
Talk:Fréchet algebra------2---
Talk:Function (mathematics)/Archive 61---------
Talk:Fundamental theorem of algebra------1---
Talk:Gamma function------1---
Talk:Gelfand pair------1---
Talk:Geometric algebra/Archive 1--1-------
Talk:Gibbs–Duhem equation--2-------
Talk:Gravitoelectromagnetism--1-------
Talk:Hamiltonian (quantum mechanics)--1-------
Talk:Harmonic mean--------1-
Talk:Hartogs number1---------
Talk:Hash table1--------2
Talk:Hilbert space/Archive 2--1-------
Talk:Hodge star operator2---------
Talk:Hunan---------1
Talk:Indifference curve22--------
Talk:Infinitary logic1---------
Talk:Information gain in decision trees--3-------
Talk:Inner measure---------1
Talk:Integrated pest management--------1-
Talk:Interest/Archive 1--------1-
Talk:Internal set theory21--------
Talk:Iterated logarithm---------2
Talk:Kármán vortex street--2-------
Talk:Lack-of-fit sum of squares--1-------
Talk:Lagrangian mechanics--2-------
Talk:Lagrangian mechanics/Archive 1--4-------
Talk:Law of the iterated logarithm---------1
Talk:Lebesgue integration2---------
Talk:Legendre transformation---1------
Talk:Let expression12---------
Talk:Limit of a function1---------
Talk:Linear least squares (mathematics)/Archive 1--1-------
Talk:Linear regression/Archive 1---------2
Talk:Line–plane intersection--3-------
Talk:Logarithm/Archive 3---------1
Talk:Logic System--1-------
Talk:Material conditional1---------
Talk:Material conditional/Archive 1-1--------
Talk:Material implication (rule of inference)-1--------
Talk:Mathematics of musical scales---------1
Talk:Matrix multiplication/Archive 1--10-------
Talk:Maxwell's equations/Archive 5--1-------
Talk:Maxwell's equations/Archive 6--26-------
Talk:Mean time between failures/Archive 1--------1-
Talk:Mereology1---------
Talk:Method of analytic tableaux1---------
Talk:Miles per gallon gasoline equivalent--------5-
Talk:Momentum--6-------
Talk:Momentum operator--1-------
Talk:Monoid-1--------
Talk:Monty Hall problem/Archive 9-1--------
Talk:Morse–Kelley set theory53--------
Talk:Multi-index notation---8------
Talk:Natural number/Archive 12---------
Talk:Newcomb's paradox/Archive 1---------1
Talk:Newton's laws of motion/Archive 3--1-------
Talk:Newton–Euler equations--2-------
Talk:Optional stopping theorem2---------
Talk:Ordinal number/Archive 226--------
Talk:Orthogonal matrix--2-------
Talk:Pair production--1-------
Talk:Passer rating---------3
Talk:Pauli equation--1-------
Talk:Percentage---------2
Talk:Plane wave---------4
Talk:Poisson's equation/Archive 1--3-------
Talk:Polychord--1-------
Talk:Polynomial ring-1--------
Talk:Population growth---------1
Talk:Position operator--11-------
Talk:Post canonical system--------1-
Talk:Potential energy--4-------
Talk:Pre- and post-test probability1---------
Talk:Pumping lemma for regular languages2---------
Talk:Pythagorean theorem/Archive 3--2-------
Talk:Quantum finite automata11--------
Talk:Quantum gravity/Archive for 2008--2-------
Talk:Quasi-sphere-1--------
Talk:Randall Munroe/Archive 1--------1-
Talk:Ransom E. Olds--------11
Talk:Real interest rate--------22
Talk:Real number/Archive 3--2-------
Talk:Receiver operating characteristic---------1
Talk:Ricci calculus/Archive 1--1-------
Talk:Ricci calculus/Archive 2--6-------
Talk:Russell's paradox2---------
Talk:Sakura Kinomoto1---------
Talk:Schrödinger equation/Archive 21---------
Talk:Schrödinger equation/Archive 3--1-------
Talk:Set (mathematics)43--------
Talk:Set-builder notation/Archive 11---------
Talk:Sieve of Eratosthenes/Archive 24---------
Talk:Sieve of Eratosthenes/Archive 31---------
Talk:Singular perturbation---1------
Talk:Slope/Archive 1---------1
Talk:Statistical hypothesis testing/Archive 1---------1
Talk:Student's t-distribution---------1
Talk:Summation21--------
Talk:Surreal number/Archive 23---------
Talk:Tarski's axioms9---------
Talk:Tautology (rule of inference)1---------
Talk:Taylor rule---------6
Talk:Tensor density3---------
Talk:Tensor/Archive 1--2-------
Talk:Third law of thermodynamics---1------
Talk:Third party (United States)/Archive 1---------1
Talk:Time complexity---------1
Talk:Titanium/Archive 1---------1
Talk:Total relation-2--------
Talk:Transfinite induction1---------
Talk:Transitive relation3---------
Talk:Transpose------1---
Talk:Two envelopes problem/Arguments--------2-
Talk:Two envelopes problem/Arguments/Archive 1--------1-
Talk:United States Treasury security---------1
Talk:Variety (universal algebra)--1-------
Talk:Vector calculus--81------
Talk:Volume fraction---------2
Talk:Von Neumann–Bernays–Gödel set theory11--------
Talk:Waterboarding/Archive 7---------1
Talk:Wave equation---3------
Talk:Wave function/Archive 8--3-------
Talk:Wave packet--2------2
Talk:Wave vector--1-------
Talk:Wavenumber--2-------
Talk:Whitehead's point-free geometry4---------
Talk:Wind power/Archive 3---------1
Talk:Work (physics)/Archives/2011/October--1-------
Talk:Work (physics)/Archives/2012/August--1-------
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Talk:Work (physics)/Archives/2013/February--1-------
Talk:Zermelo–Fraenkel set theory142--------
Talk:Čech cohomology--1-------
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User talk:78.150.63.89---------1
User talk:98.190.133.83--------1-
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User talk:Arthur Rubin/Archive 201341--------
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