Pan Galactic Division

TL;DR

This paper presents a simplified proof of a set theory result showing that an injection from a product set implies an injection between the original sets, enhancing understanding of set mappings.

Contribution

It introduces a straightforward proof of a known set theory theorem, making the concept more accessible and easier to understand.

Findings

Simplified proof of the set theory injection theorem

Clarifies the relationship between product set injections and set injections

Enhances pedagogical approaches to set theory concepts

Abstract

This is a light expository article. It explains a proof, due to Peter Doyle and Cecil Qiu, the following result from set theory. Let A and B be sets. Suppose there is an injective map from A x {0,...,n-1} into B x {0,...,n-1}. Then there is an injection from A into B. Unlike previous proofs, this one is a very simple one.