Access to the full content is only available to members of institutions that have purchased access. If you belong to such an institution, please log in or find out more about how to order.


Print

Contents

Cantor’s theorem

DOI
10.4324/9780415249126-Y027-1
DOI: 10.4324/9780415249126-Y027-1
Version: v1,  Published online: 1998
Retrieved July 16, 2019, from https://www.rep.routledge.com/articles/thematic/cantors-theorem/v-1

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.

Print
Citing this article:
Tiles, Mary. Cantor’s theorem, 1998, doi:10.4324/9780415249126-Y027-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/cantors-theorem/v-1.
Copyright © 1998-2019 Routledge.

Related Searches

Topics

Related Articles