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When the bottom type is uninhabited, a function whose return type is bottom cannot return any value, not even the lone value of a unit type.In such a language, the bottom type may therefore be known as the zero, never or empty type which, in the Curry–Howard correspondence, corresponds to falsity.
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 ,⊥)
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
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 ...
2. Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. Also used in place of \ for denoting the set-theoretic complement; see \ in § Set theory. × (multiplication sign) 1. In elementary arithmetic, denotes multiplication, and is read as times; for example, 3 × 2. 2.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
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If, for some notion of substructure, objects are substructures of themselves (that is, the relationship is reflexive), then the qualification proper requires the objects to be different. For example, a proper subset of a set S is a subset of S that is different from S, and a proper divisor of a number n is a divisor of n that is different from n.
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