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The assertion that at least one selection algorithm succeeds without presenting that algorithm _is_ the axiom of choice. By _assuming_ that program terminates
by ketralnis 5y ago
The assertion that at least one selection algorithm succeeds without presenting that algorithm _is_ the axiom of choice.
By _assuming_ that program terminates, you are yourself taking the axiom of choice.
If it _does_ terminate, then it's not an axiom anymore it's a proof.
- shadowlight 5y agoYeah, this clarifies the logic. So because the algo above doesn't terminate it is not a proof. The axiom of choice is an assumption that is neither known to be true or false.