Table of mathematical symbols by introduction date
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{{Use dmy dates|date=August 2023}}
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The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. {{Noprint inline|The table can also be ordered alphabetically by clicking on the relevant header title.}}
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Symbol
! Name ! Date of earliest use ! First author to use |
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bgcolor=#d0f0d0 align=center| —
| 14th century (approx.) | Nicole Oresme{{Cite book |last=Cajori |first=Florian |title=A History of Mathematical Notations |publisher=Dover Publications |year=1993 |location=Mineola, New York}} |
bgcolor=#d0f0d0 align=center| +
| 1360 (approx.), abbreviation for Latin et resembling the plus sign |
bgcolor=#d0f0d0 align=center| −
| 1489 (first appearance of minus sign, and also first appearance of plus sign in print) |
bgcolor=#d0f0d0 align=center| √
| radical symbol (for square root) |
rowspan=2 bgcolor=#d0f0d0 align=center| (...)
| rowspan=2| parentheses (for precedence grouping) | 1544 (in handwritten notes) |
1556 |
bgcolor=#d0f0d0 align=center| =
| 1557 |
bgcolor=#d0f0d0 align=center| .
| 1593 |
bgcolor=#d0f0d0 align=center| ×
| 1618 | rowspan=3| William Oughtred |
bgcolor=#d0f0d0 align=center| ±
| rowspan=2| 1628 |
bgcolor=#d0f0d0 align=center| ∷
|
bgcolor=#d0f0d0 align=center| n√
| radical symbol (for nth root) | 1629 |
bgcolor=#d0f0d0 align=center| <
> | strict inequality signs (less-than sign and greater-than sign) | 1631 |
rowspan=2 bgcolor=#d0f0d0 align=center| xy
| rowspan=2| superscript notation (for exponentiation) | 1636 (using Roman numerals as superscripts) |
style=border-bottom:none| 1637 (in the modern form) |
bgcolor=#d0f0d0 align=center| x
| Use of the letter x for an independent variable or unknown value. See History of algebra: The symbol x. | 1637{{Citation | first=Carl B. | last=Boyer | author-link=Carl Benjamin Boyer | title=A History of Mathematics | edition=Second | publisher=John Wiley & Sons, Inc. | year=1991 | isbn=978-0-471-54397-8 | url=https://archive.org/details/historyofmathema00boye }} |
bgcolor=#d0f0d0 align=center| √ ̅
| radical symbol (for square root) | style=border-bottom:none| 1637 (with the vinculum above the radicand) |
bgcolor=#d0f0d0 align=center| %
| 1650 (approx.) | unknown |
bgcolor=#d0f0d0 align=center| ∞
| infinity sign | 1655 |
bgcolor=#d0f0d0 align=center| ÷
| division sign (a repurposed obelus variant) | 1659 |
rowspan=2 bgcolor=#d0f0d0 align=center| ≤
≥ | rowspan=2| unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign) | 1670 (with the horizontal bar over the inequality sign, rather than below it) |
1734 (with double horizontal bar below the inequality sign) |
bgcolor=#d0f0d0 align=center| d
| differential sign | rowspan=2| 1675 | rowspan=4| Gottfried Leibniz |
bgcolor=#d0f0d0 align=center| ∫
|
bgcolor=#d0f0d0 align=center| :
| 1684 (deriving from use of colon to denote fractions, dating back to 1633) |
bgcolor=#d0f0d0 align=center| ·
| middle dot (for multiplication) | 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers) |
bgcolor=#d0f0d0 align=center| ⁄
| division slash (a.k.a. solidus) | 1718 (deriving from horizontal fraction bar, invented by Abu Bakr al-Hassar in the 12th century) |
bgcolor=#d0f0d0 align=center| ≠
| inequality sign (not equal to) | unknown | rowspan=3| Leonhard Euler |
bgcolor=#d0f0d0 align=center| x{{prime}}
| prime symbol (for derivative) | 1748 |
bgcolor=#d0f0d0 align=center| Σ
| summation symbol | 1755 |
bgcolor=#d0f0d0 align=center| ∝
| proportionality sign | 1768 |
bgcolor=#d0f0d0 align=center| ∂
| partial differential sign (a.k.a. curly d or Jacobi's delta) | 1770 |
bgcolor=#d0f0d0 align=center| ≡
| identity sign (for congruence relation) | 1801 (first appearance in print; used previously in personal writings of Gauss) | rowspan=2| Carl Friedrich Gauss |
bgcolor=#d0f0d0 align=center| [x]
| integral part (a.k.a. floor) | 1808 |
bgcolor=#d0f0d0 align=center| !
| 1808 |
bgcolor=#d0f0d0 align=center| Π
| product symbol | 1812 |
rowspan=2 bgcolor=#d0f0d0 align=center| ⊂
⊃ | rowspan=2| set inclusion signs (subset of, superset of) | 1817 |
1890 |
rowspan=2 bgcolor=#d0f0d0 align=center| |...|
| absolute value notation | 1841 |
determinant of a matrix
| 1841 | rowspan=2| Arthur Cayley |
bgcolor=#d0f0d0 align=center| ‖...‖
| matrix notation |
bgcolor=#d0f0d0 align=center| ∇
| nabla symbol (for vector differential) | 1846 (previously used by Hamilton as a general-purpose operator sign) |
bgcolor=#d0f0d0 align=center| ∩
∪ | 1888 |
bgcolor=#d0f0d0 align=center| ℵ
| aleph symbol (for transfinite cardinal numbers) | 1893 |
bgcolor=#d0f0d0 align=center| ∈
| membership sign (is an element of) | 1894 |
bgcolor=#d0f0d0 align=center| O
| 1894 |
bgcolor=#d0f0d0 align=center| {...}
| braces, a.k.a. curly brackets (for set notation) | 1895 |
bgcolor=#d0f0d0 align=center|
| Blackboard bold capital N (for natural numbers set) | rowspan=2| 1895 | rowspan=3|Giuseppe Peano |
bgcolor=#d0f0d0 align=center|
| Blackboard bold capital Q (for rational numbers set) |
bgcolor=#d0f0d0 align=center| ∃
| existential quantifier (there exists) | 1897 |
bgcolor=#d0f0d0 align=center| ·
| middle dot (for dot product) | rowspan=2| 1902 | rowspan=2| J. Willard Gibbs |
bgcolor=#d0f0d0 align=center| ×
| multiplication sign (for cross product) |
bgcolor=#d0f0d0 align=center| ∨
| logical disjunction (a.k.a. OR) | 1906 |
bgcolor=#d0f0d0 align=center| (...)
| rowspan=2| matrix notation |
bgcolor=#d0f0d0 align=center| [...]
|
bgcolor=#d0f0d0 align=center| ∮
| contour integral sign | 1917 |
bgcolor=#d0f0d0 align=center|
| Blackboard bold capital Z (for integer numbers set) | 1930 |
bgcolor=#d0f0d0 align=center| ∀
| universal quantifier (for all) | 1935 |
rowspan=2 bgcolor=#d0f0d0 align=center| →
| rowspan=2| arrow (for function notation) | 1936 (to denote images of specific elements) |
1940 (in the present form of f: X → Y) |
bgcolor=#d0f0d0 align=center| ∅
| empty set sign | 1939 | André Weil / Nicolas Bourbaki{{citation|title=The Apprenticeship of a Mathematician|first=André|last=Weil|author-link=André Weil|publisher=Springer|year=1992|isbn=9783764326500|page=114|url=https://books.google.com/books?id=73REHmJ9JNUC&pg=PA114}}. |
bgcolor=#d0f0d0 align=center|
| Blackboard bold capital C (for complex numbers set) | 1939 |
bgcolor=#d0f0d0 align=center| ∎
| end of proof sign (a.k.a. tombstone) | 1950{{Cite book | last = Halmos | first = Paul | year = 1950 | title = Measure Theory | publisher = Van Nostrand | location = New York | quote = The symbol ∎ is used throughout the entire book in place of such phrases as "Q.E.D." or "This completes the proof of the theorem" to signal the end of a proof. | pages = vi }} |
bgcolor=#d0f0d0 align=center| ⌊x⌋
⌈x⌉ | greatest integer ≤{{thin space}}x (a.k.a. floor) |
See also
Sources
{{Reflist}}
External links
- [https://www.rapidtables.com/math/symbols/Basic_Math_Symbols.html RapidTables: Math Symbols List]
- [https://mathshistory.st-andrews.ac.uk/Miller/mathsym/ Jeff Miller: Earliest Uses of Various Mathematical Symbols]
{{Mathematical symbols notation language}}