more from Herbert B. Enderton

Single Idea 13205

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice.

Gist of Idea

We can only define functions if Choice tells us which items are involved


Herbert B. Enderton (Elements of Set Theory [1977], 3:48)

Book Reference

Enderton,Herbert B.: 'Elements of Set Theory' [Posts + Telecoms 2006], p.48