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infinite set
(redirected from Infinite sets)

    Also found in: Wikipedia 0.46 sec.
(mathematics)infinite set - 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.


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Infinite wisdom A mathematician proposed a new approach to resolving a longstanding question about infinite sets of numbers (164: 139).
Mathematics & computers by Science News
The topic chosen for this purpose, "Comparing Infinite Sets within the Cantorian Set Theory", is part of an advanced mathematics course.
From "easy" to "difficult" or vice Versa: the case of infinite sets by Tsamir, Pessia / Focus on Learning Problems in Mathematics
For one thing, there's no way to simply count the elements of two infinite sets and determine which set has more.
Infinite wisdom: a new approach to one of mathematics' most notorious ... by Klarreich, Erica / Science News
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