The up tack or falsum (⊥,
\bot in
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well.
In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosper ...
, U+22A5 in
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
) is a constant
symbol
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
used to represent:
* The
truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or ''false'').
Computing
In some prog ...
'false', or a logical constant denoting a proposition in logic that is always
false
False or falsehood may refer to:
* False (logic), the negation of truth in classical logic
*Lie or falsehood, a type of deception in the form of an untruthful statement
* false (Unix), a Unix command
* ''False'' (album), a 1992 album by Gorefest
* ...
(often called "falsum" or "absurdum").
* The
bottom element
In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S that is greater than every other element of S. The term least element is defined dually, that is, it is an el ...
in
wheel theory and
lattice theory, which also represents absurdum when used for logical semantics
* The
bottom type in
type theory
In mathematics, logic, and computer science, a type theory is the formal system, formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theor ...
, which is the bottom element in the subtype relation. This may coincide with the
empty type, which represents absurdum under the
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relat ...
as well as
*
Mixed radix
Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a mu ...
decoding in the
APL programming language
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent mos ...
The
glyph
A glyph () is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A g ...
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
Dual or Duals may refer to:
Paired/two things
* Dual (mathematics), a notion of paired concepts that mirror one another
** Dual (category theory), a formalization of mathematical duality
*** see more cases in :Duality theories
* Dual (grammatical ...
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
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
of lines in
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
*
Orthogonality
In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings i ...
in
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matric ...
*
Independence
Independence is a condition of a person, nation, country, or state in which residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the s ...
of
random variables in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
*
Coprimality in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
The double tack up symbol (⫫, U+2AEB in
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...
) is a constant
symbol
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
used to represent:
*
Conditional independence
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probabil ...
of
random variables in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
See also
*
Alternative plus sign
The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, resulti ...
*
Contradiction
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle' ...
*
List of mathematical symbols
*
Tee (symbol) The tee (⊤, \top in LaTeX) also called down tack (as opposed to the up tack) or verum is a symbol used to represent:
* The top element in lattice theory.
* The truth value of being true in logic, or a sentence (e.g., formula in propositional ...
(⊤)
*
Verum The tee (⊤, \top in LaTeX) also called down tack (as opposed to the up tack) or verum is a symbol used to represent:
* The top element in lattice theory.
* The truth value of being true in logic, or a sentence (e.g., formula in propositional ...
Notes
{{Common logical symbols
Mathematical notation
Mathematical symbols
Logic symbols