Assertion: set | /r/HasProperty | dedekind-infinite
Facets:
Source sentences:
text: Until the foundational crisis of mathematics showed the need for a more careful treatment of set theory, most mathematicians assumed that a set is infinite if and only if it is Dedekind-infinite.
text: However, there exists a model of Zermelo–Fraenkel set theory without the axiom of choice (ZF) in which there exists an infinite, Dedekind-finite set, showing that the axioms of ZF are not strong enough to prove that every set that is Dedekind-finite has a finite number of elements.
text: During the latter half of the 19th century, most mathematicians simply assumed that a set is infinite if and only if it is Dedekind-infinite.