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infinite

mathematics 1. Bigger than any natural number. There are

various formal set definitions in set theory: a set X is

infinite if

(i) There is a bijection between X and a proper subset of X.

(ii) There is an injection from the set N of natural numbers

to X.

(iii) There is an injection from each natural number n to X.

These definitions are not necessarily equivalent unless we

accept the Axiom of Choice.