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You are talking about the well-ordering theorem, not the similarly named well-ordering principle. That’s exactly my confusion when I first opened this PDF.
by kccqzy 10mo ago
You are talking about the well-ordering theorem, not the similarly named well-ordering principle. That’s exactly my confusion when I first opened this PDF.
- BeetleB 10mo agoDifferent folks use different conventions. When I was taught it, they called it the principle, not theorem. You can find similar comments on the Internet (e.g. math subreddit). Here's one that acknowledges it: https://math.stackexchange.com/questions/1837836/well-ordering-principle-and-theorem https://math.stackexchange.com/questions/1837836/well-orderi... > The "well-ordering principle" has (at least) two different meanings. The first meaning is just another name for the well-ordering theorem. The second meaning is the statement that the usual relation < on the set N is a well-ordering. This statement is equivalent to the statement that ordinary induction on the natural numbers works.