"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "absurdity", 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" 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). 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 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. 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." The double tack up symbol (⫫, U+2AEB in Unicode) is a binary relation symbol used to represent:
Conditional independence of random variables in probability theory
See also Alternative plus sign Contradiction List of mathematical symbols Tee (symbol) (⊤)
Notes