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I have always had mixed feelings about this axiom. It feels "2nd level", like it should build upon simpler axioms related to the mathematical object "set" and t
by sylware 4y ago
I have always had mixed feelings about this axiom. It feels "2nd level", like it should build upon simpler axioms related to the mathematical object "set" and the mathematical object "function".
- lupire 4y agoWhat do you mean? The Axiom of Choice is a statement about a function on sets. In context, of ZF, it's equivalent to the Well Ordering Principle/Axiom and Zorn's Lemma/Axiom.
- Koshkin 4y agoThen it wouldn’t be an axiom, which it, in fact, is, being logically independent from the rest. It is considered somewhat special though, and mathematicians, being nice people, usually indicate whether they rely on it in a proof.
- sylware 4y agoYep, this is what I meant by "2nd level": it feels like it is not an axiom but a theorem.