Talk:Monsky's theorem: Difference between revisions
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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? |
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? |
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--[[Special:Contributions/2A00:1398:4:A09:249C:FBE1:9B00:2B1F|2A00:1398:4:A09:249C:FBE1:9B00:2B1F]] ([[User talk:2A00:1398:4:A09:249C:FBE1:9B00:2B1F|talk]]) 08:09, 13 May 2024 (UTC) |
--[[Special:Contributions/2A00:1398:4:A09:249C:FBE1:9B00:2B1F|2A00:1398:4:A09:249C:FBE1:9B00:2B1F]] ([[User talk:2A00:1398:4:A09:249C:FBE1:9B00:2B1F|talk]]) 08:09, 13 May 2024 (UTC) |
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:Sounds good, go for it! [[User:Melchoir|Melchoir]] ([[User talk:Melchoir|talk]]) 20:43, 13 May 2024 (UTC) |
Latest revision as of 20:43, 13 May 2024
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Problem in Step 2 in Monksy's Proof
[edit]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)
- Sounds good, go for it! Melchoir (talk) 20:43, 13 May 2024 (UTC)