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A Set of 
elements is said to be infinite if the elements of a Proper Subset 
can be put into
One-to-One correspondence with the elements of . 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.
See also Aleph-0, Aleph-1, Cardinal Number, Countably Infinite Set, Continuum, Finite, Infinite, Infinity, Ordinal Number, Transfinite Number, Uncountably Infinite Set
References
Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.
Oxford, England: Oxford University Press, p. 77, 1996.