3 ms·
Indeed - I think the claim that alpha can be expressed as p/q with some 'lowest q' seems to rest on divisibility properties.
by jameshart 11y ago
Indeed - I think the claim that alpha can be expressed as p/q with some 'lowest q' seems to rest on divisibility properties.
- jfarmer 11y agoNo, it follows directly from the fact that the positive integers are well-ordered, i.e., any set of positive integers has a least element. And in case one is tempted to think that well-ordering and divisibility are somehow equivalent, consider Presburger arithmetic[1]. It's not even possible to define a general notion of divisibility or primality in that context, but I'm almost positive the well-ordering principle holds (it's equivalent to the axiom schema of induction). [1]: https://en.wikipedia.org/wiki/Presburger_arithmetic https://en.wikipedia.org/wiki/Presburger_arithmetic