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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 13 Feb 2019
    • Report Tweet
    • Report NetzDG Violation

    Here’s a cool instance of the Banach fixed-point theorempic.twitter.com/jRaZhyiNcM

    5:43 AM - 13 Feb 2019
    • 2,119 Retweets
    • 7,055 Likes
    • Icarox nathan William Benton a_le 🌹 Bill Kristold 🇵🇹🇮🇪🇬🇷🇪🇸 Rob Jellinghaus Victor Xie Jude Molloy Nick B 🕹️
    74 replies 2,119 retweets 7,055 likes
      1. New conversation
      2. David N. Schwartz‏ @dschwa8059 13 Feb 2019
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        Replying to @fermatslibrary

        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!

        1 reply 4 retweets 101 likes
      3. Baud'Dib‏ @blahblahblah9tn 13 Feb 2019
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        Replying to @dschwa8059 @fermatslibrary

        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

        1 reply 14 retweets 152 likes
      4. 1 more reply
      1. New conversation
      2. toffetomas‏ @toffetomas 13 Feb 2019
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        Replying to @fermatslibrary

        What's the difference between Banach fixed point theorem and Brouwer fixed point theorem?

        1 reply 0 retweets 8 likes
      3. Amogh Anakru‏ @lmaogh 13 Feb 2019
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        Replying to @toffetomas @fermatslibrary

        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).

        1 reply 5 retweets 28 likes
      4. 3 more replies
      1. New conversation
      2. ヰ Kaizer‏ @KaizerDzn 13 Feb 2019
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        Replying to @fermatslibrary

        That wouldn't work if im not in my country.

        1 reply 0 retweets 46 likes
      3. Ratnesh Shukla‏ @ratneshshukla_ 13 Feb 2019
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        Replying to @KaizerDzn @fermatslibrary

        Then place a world map.

        1 reply 0 retweets 13 likes
      4. 1 more reply
      1. New conversation
      2. david‏ @david_drothler 13 Feb 2019
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        Replying to @fermatslibrary

        Vsauce made a great Video about this topichttps://youtu.be/csInNn6pfT4 

        1 reply 4 retweets 30 likes
      3. This Tweet is unavailable.
      1. New conversation
      2. Damien Del Russo‏ @ddelruss 13 Feb 2019
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        Replying to @fermatslibrary @NickSzabo4

        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.

        3 replies 0 retweets 1 like
      3. Nick Szabo  🔑‏ @NickSzabo4 13 Feb 2019
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        Replying to @ddelruss @fermatslibrary

        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.

        1 reply 0 retweets 6 likes
      4. 1 more reply

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