You are here: irt.org | FOLDOC | infinite set

<*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

FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL