Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

The Axiom of Choice: The Last Great Controversy in Mathematics

Version 1 : Received: 2 March 2021 / Approved: 3 March 2021 / Online: 3 March 2021 (13:33:33 CET)

How to cite: Hulkewicz, J. The Axiom of Choice: The Last Great Controversy in Mathematics. Preprints 2021, 2021030133 (doi: 10.20944/preprints202103.0133.v1). Hulkewicz, J. The Axiom of Choice: The Last Great Controversy in Mathematics. Preprints 2021, 2021030133 (doi: 10.20944/preprints202103.0133.v1).

Abstract

This paper explores multiple perspectives and proofs regarding the validity of what is considered to be one of the – if not THE - most controversial proofs in the field of mathematics, historical and contemporary applications alike. We consider the various explanations and equivalents of the axiom along with the more widely receptive alternatives. Furthermore, we review the resistance the axiom has encountered in various fields and its potential use in the research and expansion of said fields.

Keywords

Axiom of Choice; Zermello; Set Theory

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