The reals aren’t well-ordered.
That’s equivalent to asserting that the axiom of choice is untrue. That’s not derivable from the other axioms, and in fact the axiom of choice is often used in mathematics. (This is entirely irrelevant to the [long-dead] discussion, however.)
That’s equivalent to asserting that the axiom of choice is untrue. That’s not derivable from the other axioms, and in fact the axiom of choice is often used in mathematics. (This is entirely irrelevant to the [long-dead] discussion, however.)