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 (angiosperm ...

, 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, whi ...

) 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 co ...

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 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 ele ...

wheel theory A wheel is a type of algebra (in the sense of universal algebra) where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring. The term ''wheel'' is inspi ...

and

lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper boun ...

, which also represents absurdum when used for logical semantics * The

bottom type In type theory, a theory within mathematical logic, the bottom type of a type system is the type that is a subtype of all other types. Where such a type exists, it is often represented with the up tack (⊥) symbol. When the bottom type is emp ...

type theory In mathematics, logic, and computer science, a type theory is the 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 theory as a founda ...

, which is the bottom element in the subtype relation. This may coincide with the

empty type In type theory, the empty type or absurd type, typically denoted \mathbb 0 is a type with no terms. Such a type may be defined as the nullary coproduct (i.e. disjoint sum of no types). It may also be defined as the polymorphic type \forall t.t For ...

, 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 relati ...

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 ...

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 mo ...

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 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 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 matrices ...

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 st ...

random variables A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

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 ...

Coprimality In mathematics, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivale ...

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, "Mathe ...

The double tack up symbol (⫫, U+2AEB in

) is a constant

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 ...

Notes

{{Common logical symbols Mathematical notation Mathematical symbols Logic symbols

See also

Notes