Talk:Monsky's theorem

Problem in Step 2 in Monksy's Proof

In Step 2 it is said that "Colour each point in the square with one of three colours, depending on the 2-adic valuation of its coordinates".

I have a problem with the definite article "the", since there is not only one 2-adic valuation on the reals. There is a unique 2-adic valuation on the rationals and you can extend this (using Zorn's Lemma or something similar) to the reals, but this extension is not unique - as far as I know. Also it is problably not known to many people that a 2-adic valuation on the reals exists at all.

So I would suggest adding a step before Step 2, which could be named "Extend the 2-adic valuation of Q to a valuation on R. Then the reader would know where the valuation comes from. Any suggestions? --2A00:1398:4:A09:249C:FBE1:9B00:2B1F (talk) 08:09, 13 May 2024 (UTC)[reply]

Sounds good, go for it! Melchoir (talk) 20:43, 13 May 2024 (UTC)[reply]