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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 2 Jun 2018
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    If you pick 2 positive integers at random, the odds of them having no common divisor are 6/π² ≈ 61%pic.twitter.com/N6bJYjwEQK

    5:53 AM - 2 Jun 2018
    • 531 Retweets
    • 2,085 Likes
    • I am foxyGrey Deepak Sadulla sursha Alec Wilson Rohan Mitra Praise Alyssa~ libero
    21 replies 531 retweets 2,085 likes
      1. New conversation
      2. Théootz‏ @Totzenberger 2 Jun 2018
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        Replying to @fermatslibrary

        This is false, unfortunately, because you can't have a "uniform" probability measure on the positive integers. Here's a proof, in french.pic.twitter.com/USKMtloF7n

        1 reply 3 retweets 9 likes
      3. Gabor Gurbacs‏ @gaborgurbacs 2 Jun 2018
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        Replying to @Totzenberger @fermatslibrary

        1) Could you explain/give 1 scenario where the the proof fails? I appreciate it. 2) how about a discrete uniform probability distributions? (but I guess we have infinitely many primes so wouldn’t make sense for the proof of the general case.)

        1 reply 0 retweets 0 likes
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      2. 𝖕 | #MassTestingNowPH  ⚔️ 🛡️‏ @xdoublestar 2 Jun 2018
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        Replying to @fermatslibrary

        A bit of pedantry: you have to be very careful with the statement "at random" because a uniform distribution over an infinite set is tricky to define. But yes.

        1 reply 1 retweet 9 likes
      3. Not Just Any Willtor‏ @MightyWilltor 2 Jun 2018
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        Replying to @xdoublestar @fermatslibrary

        Is it more correct to say: The limit as n -> infinity, any two integers less than n, etc.?

        1 reply 1 retweet 2 likes
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      2. Alexis Bietti‏ @alexisbietti 2 Jun 2018
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        Replying to @fermatslibrary

        Define "at random" please. What distribution?

        1 reply 1 retweet 0 likes
      3. 𝖕 | #MassTestingNowPH  ⚔️ 🛡️‏ @xdoublestar 2 Jun 2018
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        Replying to @alexisbietti @fermatslibrary

        As per previous replies: treat this result as a limit of uniform distributions over the first N natural numbers.

        1 reply 1 retweet 3 likes
      4. 1 more reply
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      2. Jonathan .· 〽‏ @Jonzinho7 2 Jun 2018
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        Replying to @fermatslibrary

        Someone can help me, how to pass from primes to integers?pic.twitter.com/95yK1yQIG1

        0 replies 1 retweet 2 likes
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      1. Steven Francis‏ @SFrancismath 2 Jun 2018
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        Replying to @fermatslibrary

        The reciprocal of this number is in your yearbook, if I signed it.

        0 replies 0 retweets 3 likes
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      2. 𝖕 | #MassTestingNowPH  ⚔️ 🛡️‏ @xdoublestar 2 Jun 2018
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        Replying to @Kderango @fermatslibrary

        Yes, the reciprocal. And it all has to do with Euler products. This presentation is a bit loose but that's the idea.

        0 replies 1 retweet 1 like
      3. End of conversation

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