Talk:Axiomatic introduction to the Real Numbers

Interesting resource, I look forward to reading it. While I've studied Rudin's Principles of Mathematical Analysis (at least up to around chapter 7 or 8) and did many of the exercises, I actually don't remember his construction of the reals (using Dedekind Cuts) very well and you've inspired me to have a look at it. Strictly speaking, it's incorrect to use ${\sqrt {2}}$ in the context of a proof before you've constructed the reals, i.e. shown the existence of an ordered field with the LUB property containing Q. See Rudin page 2 for a proof that p^2=2 has no solution in Q that does not make reference to ${\sqrt {2}}$. AP295 (discuss • contribs) 08:19, 6 December 2023 (UTC)

At any rate, I do recommend picking up a copy of Rudin. The cheap paperback I have seems more expensive than I remember but it looks like there are cheaper reprints available. I remember liking it, though I've somewhat forgotten much of what I learned. I suppose it's good to periodically review if you want to remember things offhand. In my edition his construction of the reals is in the appendix of chapter 1, and I probably skipped it if I'm honest. AP295 (discuss • contribs) 08:31, 6 December 2023 (UTC)