a set that can be put on a one-to-one correspondence with a proper subset of itself
a set that does not have finitely many elements
a set which is equivilant to a proper subset of itself
a set with an infinite number of elements, while a finite set is a set with a finite number of elements
A set that contains an uncountable number of elements.
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.