A set of elements S is said to be infinite if the elements of a proper subset S' can be put into one-to-one correspondence with the elements of S. An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.

aleph-0 | aleph-1 | cardinal number | continuum | countably infinite | finite set | infinite | infinity | ordinal number | transfinite number | uncountably infinite