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michael_nielsen's profile
michael_nielsen
michael_nielsen
michael_nielsen
@michael_nielsen

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michael_nielsen

@michael_nielsen

Searching for the numinous. Co-purveyor of https://quantum.country/ 

San Francisco, CA
michaelnielsen.org
Joined July 2008

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    1. michael_nielsen‏ @michael_nielsen Jul 8
      • Report Tweet

      michael_nielsen Retweeted Dan Luu

      Lovely lay explanation of what it means for a number to be transcendental.https://twitter.com/danluu/status/1147983323483922433 …

      michael_nielsen added,

      Dan Luu @danluu
      Really nice answer to the question "in layman's terms, what exactly does it mean to be transcendental? How would a transcendental number be different from an ordinary number, say 5": https://math.stackexchange.com/a/1686299/18947  pic.twitter.com/IbOdO1Yklj
      Show this thread
      3 replies 17 retweets 137 likes
      Show this thread
    2. michael_nielsen‏ @michael_nielsen Jul 8
      • Report Tweet

      I can't resist mentioning a proof e is irrational. Suppose for a contradiction that it's not. Then e = 1 + 1/2! + 1/3! + ... = p / q for positive integers p & q. Multiply both side by q! & you see 1/(q+1) + 1/(q+1)(q+2)+... is an integer. But it's easily shown to be > 0 & < 1 QED

      2 replies 3 retweets 33 likes
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    3. RePopulus‏ @PopulusRe Jul 8
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      Replying to @michael_nielsen

      Same idea, but more technical for pi...

      1 reply 0 retweets 0 likes
      michael_nielsen‏ @michael_nielsen Jul 8
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      Replying to @PopulusRe

      I don't know of a similar proof for pi. What's the proof using the same idea?

      2:17 AM - 8 Jul 2019
      3 replies 0 retweets 0 likes
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        1. RePopulus‏ @PopulusRe Jul 8
          • Report Tweet
          Replying to @michael_nielsen

          You sp'it a série in two parts, you make the same hypothesis, and you make for the two parts the same kind of majoration. But it is really more technical for pi

          1 reply 0 retweets 0 likes
        2. RePopulus‏ @PopulusRe Jul 8
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          Replying to @PopulusRe @michael_nielsen

          You can find this proof in the classical book of Hardy

          0 replies 0 retweets 0 likes
          3. End of conversation
        1. RePopulus‏ @PopulusRe Jul 8
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          Replying to @michael_nielsen

          You can find the Hermite's proof here: https://arxiv.org/abs/1512.02791 

          0 replies 0 retweets 0 likes
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        1. RePopulus‏ @PopulusRe Jul 8
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          Replying to @michael_nielsen

          Another proof, inspirated by Hermite. I don't remember exactly if it is the proof in my last edition of Hardy's book: http://www.ams.org/journals/bull/1947-53-06/S0002-9904-1947-08821-2/S0002-9904-1947-08821-2.pdf …

          0 replies 0 retweets 0 likes
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