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.
Script error: No such module "anchor".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
Notes
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- ↑ a b Script error: No such module "citation/CS1".
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- ↑ Unicode 4.0 did defined "UP TACK = orthogonal to = perpendicular = base, bottom."
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