High Quality Content by WIKIPEDIA articles! In mathematics, a singleton is a set with exactly one element. For example, the set {0} is a singleton. Note that a set such as {{1, 2, 3}} is also a singleton: the only element is a set (which itself is however not a singleton). A set is a singleton if and only if its cardinality is 1. In the set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {0}. In axiomatic set theory, the existence of singletons is a consequence of the axiom of pairing: for any set A that axiom applied to A and A asserts the existence of {A,A}, which is the same as the singleton {A} (since it contains A, and no other set, as element). If A is any set and S is any singleton, then there exists precisely one function from A to S, the function sending every element of A to the one element of S.

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