Definition of finite in set theory
42849
Is it true that $\omega=\{0,1,2,3,\ldots\}$ in ZFC?
147213
Prove that finite unions of compact sets are compact
125683
Power set of a finite set is finite proof, no cardinality of power set
122814
Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
15438
do all uncountable sets have same cardinality as real numbers?
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
84936
The set of all finite sequences of members of a countable set is also countable
81843
Sequences of sets property
66334
How is every subset of the set of reals with the finite complement topology compact?
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
94413
Proving Dedekind finite implies finite assuming countable choice
9021
An infinite subset of a countable set is countable
32795
Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.
97064
Dense set in an infinite cofinite space
45878
Elementary Set Theory: Ordinals, Well Orderings and Isomorphisms
68230
The cardinality of a countable union of sets with less than continuum cardinality
78117
Closed property of nonempty finite set