ProofWiki talk:Potw

Please remember to proofread what you choose as the proof of the week before putting it up. It looks bad to have errors in the first proof that people see when they come to the page. I found a relatively minor typographical error in the Cantor-Bernstein-Schroeder Theorem after it was made POTW. --cynic 14:17, 14 September 2008 (UTC)

Well that told me. Well caught.

Having said that, we're running out of "important" proofs to select to be POTW. I'm a bit busy laying some of the groundwork, but I'm working up to some more major results. I'd be interested to know what anyone else has in mind for proofs they'd like to add to this site. ;-) --Matt Westwood 14:53, 14 September 2008 (UTC)

I'll probably put up proofs of the equivalence of the Well Ordering Principle, the Principle of Mathematical Induction, and the Principle of Strong Induction later tonight. Mostly, I just put up whatever proofs I'm working on in my math classes. On a related note, should I put up Peano's Axioms of the Natural Numbers in the Axioms namespace, or do they follow in some fashion out of those that you already put? And if they are going up, any preferences on whether Induction or Well Ordering should be taken as an Axiom? --cynic 17:57, 14 September 2008 (UTC)

I've got no problems you putting up any proofs of anything that I may or may not be approaching (I expect to get around to everything in my vast library sooner or later). Peano's Axioms would be good in the Axioms namespace, as they form a good starting-point to approach the number systems from and are basically stand-alone. (It is of course possible to deduce that a structure based from them can also be created from the ZF axioms, and I'll be getting there sometime soon, but they still have the "feel" of being axiomatic.) As for the Principle of Mathematical Induction, I expect to be able to prove the validity of that from first principles in a few weeks or so, so feel free to bear that in mind.

Feel free to formulate Peano in whatever way you're most comfortable with, but the most basic way I've seen them formulated doesn't need to invoke the concept of well-ordering - the latter can be deduced.

Basically, just do what you wanna do - my view is: get stuff in there, we can polish it later once we have enough background of other stuff. We need more "big name" proofs, surely - I'm just fiddling around with all those nuts and bolts that I find so fascinating. --Matt Westwood 18:49, 14 September 2008 (UTC)