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Cantor’s theorem

DOI: 10.4324/9780415249126-Y027-1
Version: v1,  Published online: 1998
Retrieved June 24, 2024, from

Article Summary

Cantor’s theorem states that the cardinal number (‘size’) of the set of subsets of any set is greater than the cardinal number of the set itself. So once the existence of one infinite set has been proved, sets of ever increasing infinite cardinality can be generated. The philosophical interest of this result lies (1) in the foundational role it played in Cantor’s work, prior to the axiomatization of set theory, (2) in the similarity between its proof and arguments which lead to the set-theoretic paradoxes, and (3) in controversy between intuitionist and classical mathematicians concerning what exactly its proof proves.

Citing this article:
Tiles, Mary. Cantor’s theorem, 1998, doi:10.4324/9780415249126-Y027-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2024 Routledge.

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