The axiom of choice: what it asserts,
why it looks obvious, what it lets you
prove, what pathologies follow — and
what mathematics looks like without it,
and why most keep it.

What the Axiom of Choice Costs

The trade — including the pathologies it buys.

Prompt

Explain the axiom of choice: what it asserts, why it looks obvious, what it lets you prove, and what pathological results follow. Then explain what mathematics looks like without it and why most mathematicians keep it.