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.
Infinite Set
See also
Aleph-0, Aleph-1, Cardinal Number, Countably Infinite, Continuum, Finite Set, Infinite, Infinity, Ordinal Number, Transfinite Number, Uncountably InfiniteExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Infinite SetCite this as:
Weisstein, Eric W. "Infinite Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InfiniteSet.html