Up tack

The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode^[1]) is a constant symbol used to represent:

• The truth value 'false', or a logical constant denoting a proposition in logic that is always false (often called "falsum" or "absurdum").
• 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).^{[citation needed]} 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^[2] 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^[3]. 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."^[4]

The double tack up symbol (⫫, U+2AEB in Unicode^[1]) is a binary relation symbol used to represent:

• Conditional independence of random variables in probability theory^[5]

See also

• Alternative plus sign
• Contradiction
• List of mathematical symbols
• Tee (symbol) (⊤)