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What (who) is infinite set - definition
SET WITH INFINITE CARDINALITY
Infinite sets; Infinite cardinality; Infinite (cardinality)
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)
Infinite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
Dedekind-infinite set
PROPER SUBSET B OF A THAT IS EQUINUMEROUS TO A
Dedekind infinite; Dedekind-infinite; Dedekind finite; Dedekind finite set; Dedekind-finite set; Dedekind-finite; Dedekind infinity; Directly finite ring; Dedekind finite ring; Didekind infinite
In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A.
Wikipedia
Infinite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
