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arthur_affect's profile
Arthur Chu
Arthur Chu
Arthur Chu
Verified account
@arthur_affect

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Arthur ChuVerified account

@arthur_affect

Mad genius, comedian, actor, and freelance voiceover artist broadcasting from the distant shores of Lake Erie (he/him)

Broadview Heights, Ohio
arthur-chu.com
Joined August 2009

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    1. Dieu‏ @hllizi 7 Aug 2020
      Replying to @arthur_affect @lawnerdbarak and

      I don't know much about non-standard analysis either, but if I'm not completely mistaken here you'll have an infinity of infinite numbers in that system because, as you pointed out, e.g. 1 + x != x no matter what.

      2 replies 1 retweet 4 likes
    2. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @hllizi @lawnerdbarak and

      Right, like the reason for the term "hyperreal" is they're "adjacent" to the real numbers, constructed directly from doing math with them, and instead of just going "ERROR" when you get an infinite term continuing on with the infinite term attached to real terms

      2 replies 1 retweet 8 likes
    3. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @arthur_affect @hllizi and

      So there's no actual, distinct number ∞ you can use by itself, just in the course of doing an integration you might get an x + n term where x is real and n is an unbounded, non-standard term But you can't ever compare that n to any other n you get doing something else

      4 replies 1 retweet 5 likes
    4. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @arthur_affect @hllizi and

      Hence you just roll with paradoxical ideas like n +1 is higher than n, as is 2n or n^2, even though n supposedly is ∞

      3 replies 1 retweet 2 likes
    5. Dieu‏ @hllizi 7 Aug 2020
      Replying to @arthur_affect @lawnerdbarak and

      The problem seems to me rather that one starts with vage preconceptions of ∞ as some definite quantity, an idea that, I think, has never worked.

      1 reply 0 retweets 2 likes
    6. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @hllizi @lawnerdbarak and

      Well that's just it, Cantor did invent rules for treating ∞ as a "definite quantity" and they do work, they just don't work the way you'd expect working with real numbers (because it's not a real number)

      3 replies 1 retweet 6 likes
    7. Baal Ska Tov‏ @mssilverstein 7 Aug 2020
      Replying to @arthur_affect @hllizi and

      Well - a number that you can do math with. I'm not sure that qualifies as a 'definite quantity' though.

      1 reply 0 retweets 2 likes
    8. Dieu‏ @hllizi 7 Aug 2020
      Replying to @mssilverstein @arthur_affect and

      I'd certainly regard alelph 0 as a definite quantity as I meant it. My point is just that, as you climb up the power set hierarchy, you get greater quantities but - of course - all of them are infinite. So there is not just one single quantity "infinite".

      1 reply 0 retweets 1 like
    9. Dieu‏ @hllizi 7 Aug 2020
      Replying to @hllizi @mssilverstein and

      To put it like this: "larger than three" is not a definite quantity. And in a similar sense, the exploration of the transfinite revealed that - if you want to accept such a thing at all - neither is "greater than every natural number".

      1 reply 0 retweets 0 likes
    10. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @hllizi @mssilverstein and

      Yeah fair enough, although what Cantor was trying to do was specifically establish that there was a specific number that referred to all of a specific "kind of infinity"

      1 reply 0 retweets 2 likes
      Arthur Chu‏Verified account @arthur_affect 7 Aug 2020
      Replying to @arthur_affect @hllizi and

      Like that aleph-null is the size of the set of all natural numbers, and all even numbers, and all prime numbers, and all rational numbers, and all the powers of ten You can use the = sign to say these are all the same number

      7:03 AM - 7 Aug 2020
      • 2 Likes
      • Hoydenne Dieu
      1 reply 0 retweets 2 likes
        1. Dieu‏ @hllizi 7 Aug 2020
          Replying to @arthur_affect @mssilverstein and

          OK, I think now we're on the same page again.

          0 replies 0 retweets 0 likes
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