denumerably infinite

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time is called a countably infinite (or denumerably infinite) set. Once one countable set S is given, any other set which can be put into a one-to-one correspondence with S is also countable. Countably infinite sets have cardinal number aleph-0.

aleph-0 | aleph-1 | Cantor diagonal method | cardinal number | continuum | continuum hypothesis | countable set | Hilbert hotel | infinite | infinity | uncountably infinite