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infinite set definition
<mathematics> A set with an infinite number of elements.
There are several possible definitions, e.g.
(i) ("Dedekind infinite") A set X is infinite if there exists
a bijection (one-to-one mapping) between X and some proper
subset of X.
(ii) A set X is infinite if there exists an injection from N
(the set of natural numbers) to X.
In the presence of the Axiom of Choice all such definitions
are equivalent.
(1995-03-27)
Nearby terms:
Infinite Impulse Response « infinite loop « Infinite Monkey Theorem « infinite set » infinity » infix notation » infix syntax
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