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## Set Theory
## RelationsA Relation R relating A to B is a set of tuples (a,b) where a∈A, b∈B (which tuples these are defines a specific relation). ## FunctionsA Function f : A -> B assigns, for some elements of A, an element of the set A (that set is called the domain) to an element of the set B (that set is called the codomain). A Function is a Relation such that if a is related to b, then a is not related to any other element the same time. ## Partial FunctionsA Function f does not have to assign a value for each element of A (the domain). If it doesn't, it's called a Partial Function. ## Total FunctionsA Function f does not have to assign a value for each element of A. If it does, it's called a Total Function. ## RangeThe range is the set of values that result from applying f (pointwise) to all elements of the domain. The range is not (necessarily) the codomain. ## ImageThe Image of a Function is the set of values that result from applying f (pointwise) to some specified set (not necessarily the entire domain). Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |