If the the real numbers for instance have a well-ordering, can you not form a bijection from the reals to the natural numbers? Simply map the smallest of the reals to 0, and then iteratively map successors to each other. What is it I'm missing here?
2026-04-08 15:00:09.1775660409
How does Cantor's diagonal argument not contradict the well-ordering theorem?
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Such a map, from an infinite well ordered set to the natural numbers, might not be defined for all members of the intended domain. In fact it certainly will not if that domain has order type greater than omega.