Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A refinement of Cantor’s theorem
HTML articles powered by AMS MathViewer

by G. Kirmayer PDF
Proc. Amer. Math. Soc. 83 (1981), 774 Request permission

Abstract:

It is shown that there is no surjection from the one-element subsets of a set containing an infinite co-infinite set to the infinite co-infinite subsets of that set. It is also shown that there is no surjection from the one-element subsets of an infinite set to the infinite subsets of that set. The proof can be formalized in a subtheory of both Zermelo Set Theory and New Foundations (and thus makes no use of the Axiom of Choice).
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A99
  • Retrieve articles in all journals with MSC: 04A99
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 774
  • MSC: Primary 04A99
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630053-5
  • MathSciNet review: 630053