up tack
{{Short description|Symbol used in mathematics and logic}}
{{refimprove|section|date=May 2014}}
"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode{{cite web| title=Mathematical Operators – Unicode| url=https://www.unicode.org/charts/PDF/U2200.pdf| access-date=2013-07-20}}) that is also called "bottom",{{Cite book |last=Giunchiglia |first=Enrico |url=https://www.google.com.br/books/edition/Theory_and_Applications_of_Satisfiabilit/PSgGCAAAQBAJ |title=Theory and Applications of Satisfiability Testing: 6th International Conference, SAT 2003. Santa Margherita Ligure, Italy, May 5-8, 2003, Selected Revised Papers |last2=Tacchella |first2=Armando |date=2004-02-24 |publisher=Springer |isbn=978-3-540-24605-3 |pages=507 |language=en}} "falsum",{{Cite book |last=Ribeiro |first=Henrique Jales |url=https://www.google.com.br/books/edition/Inside_Arguments/QU4sBwAAQBAJ |title=Inside Arguments: Logic and the Study of Argumentation |date=2012-04-25 |publisher=Cambridge Scholars Publishing |isbn=978-1-4438-3931-0 |pages=382 |language=en}} "absurdum",{{Cite book |last=Gallier |first=Jean |url=https://www.google.com.br/books/edition/Discrete_Mathematics/HXSjIP0OgCUC |title=Discrete Mathematics |date=2011-02-01 |publisher=Springer Science & Business Media |isbn=978-1-4419-8047-2 |pages=4 |language=en}} or "the absurdity symbol",{{Cite journal |last=Makridis |first=Odysseus |date=2022 |title=Symbolic Logic |url=https://link.springer.com/book/10.1007/978-3-030-67396-3 |journal=Palgrave Philosophy Today |language=en |pages=207 |doi=10.1007/978-3-030-67396-3 |issn=2947-9339|url-access=subscription }}{{Cite book |last=Tennant |first=Neil |url=https://www.google.com.br/books/edition/Introducing_Philosophy/VbagBgAAQBAJ |title=Introducing Philosophy: God, Mind, World, and Logic |date=2015-02-11 |publisher=Routledge |isbn=978-1-317-56087-6 |pages=179 |language=en}} depending on context. It is used to represent:
- The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity symbol" come from this context.)
- The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics
- The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence
- The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r0,⊥)
as well as
- Mixed radix decoding in the APL programming language
The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (the word "tee" in reverse).{{Cite book |last=Church |first=Alonzo |url=https://www.google.com.br/books/edition/The_Journal_of_Symbolic_Logic/gpE0AAAAIAAJ? |title=The Journal of Symbolic Logic |last2=Langford |first2=Cooper Harold |date=1957 |publisher=Association for Symbolic Logic. |pages=41 |language=en}}{{Cite book |last=Smullyan |first=Raymond M. |title=Forever undecided: a puzzle guide to Gödel |date=1987 |publisher=Knopf |isbn=978-0-394-54943-9 |edition=1 |location=New York, N.Y |pages=57}} Tee plays a complementary or dual role in many of these theories.
{{Anchor|Perpendicular symbol}}The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent:
- Perpendicularity of lines in geometry
- Orthogonality in linear algebra
- Independence of random variables in probability theory
- Coprimality in number theory
Historically, in character sets before Unicode 4.1 (March 2005), such as Unicode 4.0{{cite web |title=The Unicode Standard, Version 4.0 (Archived Code Charts) |url=https://www.unicode.org/versions/Unicode4.0.0/CodeCharts.pdf |access-date=25 April 2025}} and JIS X 0213, the perpendicular symbol was encoded with the same code point as the up tack, specifically U+22A5 in Unicode 4.0.[https://www.unicode.org/versions/Unicode4.0.0/CodeCharts.pdf Unicode 4.0] did defined "UP TACK = orthogonal to = perpendicular = base, bottom." This overlap is reflected in the fact that both HTML entities ⊥ and ⊥ refer to the same code point U+22A5, as shown in the HTML entity list. In March 2005, Unicode 4.1 introduced the distinct symbol "⟂" (U+27C2 "PERPENDICULAR") with a reference back to ⊥ (U+22A5 "UP TACK") and a note that "typeset with additional spacing."{{cite web |title=Miscellaneous Mathematical Symbols-A, Range: 27C0–27EF – The Unicode Standard, Version 4.1 |url=https://www.unicode.org/charts/PDF/Unicode-4.1/U41-27C0.pdf |access-date=25 April 2025}}
The double tack up symbol (⫫, U+2AEB in Unicode) is a binary relation symbol used to represent: