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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.

2. The length of a line extended indefinitely.

See also infinite loop, infinite set.

[Jargon File]



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inference
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infimum
ABC
aleph 0
Axiom of Choice
Banach space
bit bang
Infinite Impulse Response
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Infinite Monkey Theorem
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infinity


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