A set is finite if it can be listed bijectively as the elements of {1,...,n} for some n in the natural numbers with zero; otherwise it is infinite.
In the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, let be a set, and let be as in Intervals of Natural Numbers §segment.
is finite if there are and a bijection from onto ; otherwise is infinite.
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