Function Spaces
The set of all functions from a set X to a set Y is denoted by X → Y, by, or by YX. The latter notation is motivated by the fact that, when X and Y are finite and of size |X| and |Y|, then the number of functions X → Y is |YX| = |Y||X|. This is an example of the convention from enumerative combinatorics that provides notations for sets based on their cardinalities. If X is infinite and there is more than one element in Y then there are uncountably many functions from X to Y, though only countably many of them can be expressed with a formula or algorithm.
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