1. Conway and Doyle Can Divide by Three, But I Can't.
- Author
-
Lutz, Patrick
- Subjects
CARDINAL numbers ,LINEAR orderings ,NATURAL numbers ,SET theory ,ORDERED sets - Abstract
The article explores the concept of division by a natural number without the axiom of choice in mathematics. It introduces the principles of "shoe division" and "sock division" as alternative versions of division by n. The text discusses the relationship between sock division and multiplication, presenting a theorem that proves their equivalence. It also explores the implications of sock division for bundles and the different interpretations of multiplication without the axiom of choice. The article concludes with a question about the relationship between divisibility and sock division in ZF set theory. [Extracted from the article]
- Published
- 2024
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