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. 2. The length of a line extended indefinITely. See also infinITe loop, infinITe set. [Jargon File] (1995-03-29)