infinite set
set with infinite cardinality
Dedekind-infinite set
proper subset B of A that is equinumerous to A
amorphous set
infinite set which is not the disjoint union of two infinite subsets (in models of set theory in which the axiom of choice fails)
countably infinite set
set with the same cardinality as the set of natural numbers
uncountable set
set with cardinal number larger than that of the set of all natural numbers