Talk:Method of Infinite Descent

As stated, the proof of this method requires the Axiom of Countable Choice, which is independent of ZF.

It could be refactored to instead use Well-Ordering Principle directly, keep the set of all smaller elements, or prove a long enough finite prefix of the sequence in the proof. CircuitCraft (talk) 12:44, 7 February 2023 (UTC)


 * I can't see why Axiom of Countable Choice could be needed. Given that $\map P {n_\alpha}$ holds for some arbitrary (finite) $n_\alpha$, there is only a finite number of numbers less than it. And choice from a finite set can be done in ZF, surely?
 * But in any case, we already do use Well-Ordering Principle . I don't understand any of this mathermetics stuff. --prime mover (talk) 18:55, 7 February 2023 (UTC)