## infinite

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]Last updated: 1995-03-29

### Nearby terms:

inference rule ♦ infimum ♦ **infinite** ♦ Infinite Impulse Response ♦ infinite loop

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