nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqypren5k53ms4x26agn2qg4anqpe3a7zuy39qjjd5slavzskqn2qgxcaztfm (nprofile…ztfm) Since we are chatting, I might as well add tangentially that it is possible to stumble upon independent statements even in recreational mathematics (!). I learnt the following cute example from David Madore:
Consider the following game where Eve and Adam are allied, but cannot communicate aside from agreeing on a strategy in advance. Eve receives two distinct natural numbers and chooses one of them. Adam receives this number and makes a finite number of guesses. They win when the second number was in the guesses.
Easy exercise: exhibit a winning strategy for Eve and Adam.
Now modify the game to replace natural numbers with real numbers.
Exercise: show that Eve and Adam have no winning strategy.
Further modify the game so Eve receives *three* real numbers and chooses *two* of them which are transmitted to Adam. He must make finitely many guesses for the third one.
Challenging exercise: show that Eve and Adam have a winning strategy if and only if the continuum hypothesis holds.
Jean Abou Samra (new account)
npub14p…htzwd
2025-11-18 10:40:09 UTC
in reply to nevent1q…8k4z
Author Public Key
npub14pv6xjcsz2qa6tctew034s5wsj5p2xuh65q86qe6gpegaslstc6qjhtzwdPublished at
2025-11-18 10:40:09 UTCEvent JSON
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