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A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection). A function is bijective if and only if every possible image is mapped to by exactly one argument. [1] This equivalent condition is formally expressed as follows:
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. [ 1 ] [ 2 ] Set-valued functions are used in a variety of mathematical fields, including optimization , control theory and game theory .
Injective function: has a distinct value for each distinct input. Also called an injection or, sometimes, one-to-one function. In other words, every element of the function's codomain is the image of at most one element of its domain. Surjective function: has a preimage for every element of the codomain, that is, the codomain equals the image.
Codomain – Target set of a mathematical function; Range of a function – Subset of a function's codomain; Image (mathematics) – Set of the values of a function; Injective function – Function that preserves distinctness; Surjection – Mathematical function such that every output has at least one input; Bijection – One-to-one correspondence
For a value of 1 it would return "one". For a value of 2 it would return "two". For the values 3, 4 or 5 it would return "range 3–5". For any other value, or a null value, it would return "other". However, in many cases, the #switch function is a multi-line form, with each branch on a different line, as follows:
The smallest such set is denoted by N, and its members are called natural numbers. [2] The successor function is the level-0 foundation of the infinite Grzegorczyk hierarchy of hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc. It was studied in 1986 in an investigation involving generalization of the ...
In mathematics, a subadditive set function is a set function whose value, informally, has the property that the value of function on the union of two sets is at most the sum of values of the function on each of the sets.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.