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Infinite Set


A set of elements S is said to be infinite if the elements of a proper subset S^' can be put into one-to-one correspondence with the elements of S. 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, Continuum, Finite Set, Infinite, Infinity, Ordinal Number, Transfinite Number, Uncountably Infinite

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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 Set

Cite this as:

Weisstein, Eric W. "Infinite Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InfiniteSet.html

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