> So randomness seems like a good fit for "choice" here, no? The axiom of choice is exactly the thing that tells us that we can make "random" choices. The way

> So randomness seems like a good fit for "choice" here, no? The axiom of choice is exactly the thing that tells us that we can make "random" choices. The way set theory works is that you have axioms to talk about intuitions of sets. So you might say that such a reasonable intuition is that we can make "make unlimited random choices", but this is exactly the axiom of choice! It's not about a choice from an infinity but an infinity of choices.