Up tack
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"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode[1]) that is also called "bottom",[2] "falsum",[3] "absurdum",[4] or "the absurdity symbol",[5][6] 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).[7][8] Tee plays a complementary or dual role in many of these theories.
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[9] 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[10]. 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."[11]
The double tack up symbol (⫫, U+2AEB in Unicode[1]) is a binary relation symbol used to represent:
See also
[edit]Notes
[edit]- ^ a b "Mathematical Operators – Unicode" (PDF). Retrieved 2013-07-20.
- ^ Giunchiglia, Enrico; Tacchella, Armando (2004-02-24). Theory and Applications of Satisfiability Testing: 6th International Conference, SAT 2003. Santa Margherita Ligure, Italy, May 5-8, 2003, Selected Revised Papers. Springer. p. 507. ISBN 978-3-540-24605-3.
- ^ Ribeiro, Henrique Jales (2012-04-25). Inside Arguments: Logic and the Study of Argumentation. Cambridge Scholars Publishing. p. 382. ISBN 978-1-4438-3931-0.
- ^ Gallier, Jean (2011-02-01). Discrete Mathematics. Springer Science & Business Media. p. 4. ISBN 978-1-4419-8047-2.
- ^ Makridis, Odysseus (2022). "Symbolic Logic". Palgrave Philosophy Today: 207. doi:10.1007/978-3-030-67396-3. ISSN 2947-9339.
- ^ Tennant, Neil (2015-02-11). Introducing Philosophy: God, Mind, World, and Logic. Routledge. p. 179. ISBN 978-1-317-56087-6.
- ^ Church, Alonzo; Langford, Cooper Harold (1957). The Journal of Symbolic Logic. Association for Symbolic Logic. p. 41.
- ^ Smullyan, Raymond M. (1987). Forever undecided: a puzzle guide to Gödel (1 ed.). New York, N.Y: Knopf. p. 57. ISBN 978-0-394-54943-9.
- ^ "The Unicode Standard, Version 4.0 (Archived Code Charts)" (PDF). Retrieved 25 April 2025.
- ^ Unicode 4.0 did defined "UP TACK = orthogonal to = perpendicular = base, bottom."
- ^ "Miscellaneous Mathematical Symbols-A, Range: 27C0–27EF – The Unicode Standard, Version 4.1" (PDF). Retrieved 25 April 2025.
- ^ "Conditional independence notation". 27 March 2020.
