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In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
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 ( r 0 ,⊥)
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.
In subtyping systems, the bottom type is a subtype of all types. [1] It is dual to the top type, which spans all possible values in a system. If a type system is sound, the bottom type is uninhabited and a term of bottom type represents a logical contradiction
It is emphasized that the definition of depends on context. For instance, had L {\displaystyle L} been declared as a subset of Y , {\displaystyle Y,} with the sets Y {\displaystyle Y} and X {\displaystyle X} not necessarily related to each other in any way, then L ∁ {\displaystyle L^{\complement }} would likely mean Y ∖ L {\displaystyle Y ...
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A term's definition may require additional properties that are not listed in this table. In mathematics , a binary relation R is called well-founded (or wellfounded or foundational [ 1 ] ) on a set or, more generally, a class X if every non-empty subset S ⊆ X has a minimal element with respect to R ; that is, there exists an m ∈ S such that ...