Reminds me of the great Borges story about a country where mapmakers were so obsessed with creating an accurate map that the map itself eventually became the size of the country! Borges, meet Banach!
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Original elaboration was Lewis Carroll's. The Borges story you're thinking of is On Exactitude in Science https://en.wikipedia.org/wiki/On_Exactitude_in_Science …pic.twitter.com/YcSew4AUIA
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What's the difference between Banach fixed point theorem and Brouwer fixed point theorem?
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They both guarantee a fixed point of a function but give different existence conditions. Brouwer has very strong conditions on the domain (must be homeomorphic to a convex set, and compact) while having weaker conditions on the function itself (continuous only).
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That wouldn't work if im not in my country.
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Then place a world map.
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The orientation of the map doesn’t matter? I feel like if I’m in Hawaii and put down a US map with north facing south that no point would be touching. But I’m probably wrong. I need to see the proof :-) Thanks for posting.
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The matching point would just move a bit further east in your map room. Keep rotating your map and they'd form a circle on your floor.
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