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ModelOfTheory's profile
Model Of Theory
Model Of Theory
Model Of Theory
@ModelOfTheory

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Model Of Theory

@ModelOfTheory

ZFC, THIS.

Joined July 2016

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    Model Of Theory‏ @ModelOfTheory Jun 29

    Addition is an operation on unordered pairs of numbers. Multiplication is an operation on ordered pairs of numbers, but is commutative.

    12:16 PM - 29 Jun 2018
    • 2 Retweets
    • 15 Likes
    • Davidescu the Romanian spuzz Σ:3 sina motamedi Ben Goodman Spe Akash A Kamble John Malkovich Unit Of Selection
    3 replies 2 retweets 15 likes
      1. New conversation
      2. Davidescu the Romanian‏ @yehezkeldavid Jul 18
        Replying to @ModelOfTheory @UnitOfSelection

        This would be true if there were such thing as an “unordered pair”

        1 reply 0 retweets 0 likes
      3. Model Of Theory‏ @ModelOfTheory Jul 18
        Replying to @yehezkeldavid @UnitOfSelection

        There is.

        1 reply 0 retweets 0 likes
      4. Davidescu the Romanian‏ @yehezkeldavid Jul 18
        Replying to @ModelOfTheory @UnitOfSelection

        An unordered pair is just an equivalence class of ordered pairs.

        1 reply 0 retweets 0 likes
      5. Davidescu the Romanian‏ @yehezkeldavid Jul 18
        Replying to @yehezkeldavid @ModelOfTheory @UnitOfSelection

        Try writing the letters A and B without writing them in a particular order

        1 reply 0 retweets 0 likes
      6. Model Of Theory‏ @ModelOfTheory Jul 18
        Replying to @yehezkeldavid @UnitOfSelection

        The symbol is not the referent.

        1 reply 0 retweets 0 likes
      7. Davidescu the Romanian‏ @yehezkeldavid Jul 18
        Replying to @ModelOfTheory @UnitOfSelection

        What is the relation between the symbol and the referent?

        0 replies 0 retweets 0 likes
      8. End of conversation
      1. New conversation
      2. Amateur Slacker‏ @noop_noob Jun 29
        Replying to @ModelOfTheory

        What?

        1 reply 0 retweets 1 like
      3. Michael Burge‏ @TheMichaelBurge Jun 29
        Replying to @noop_noob @ModelOfTheory

        Disjoint union corresponds to addition and works for any two sets. Swapping them yields an equal set. Set product requires one set to be designated as an "indexing set". Swapping them is set-isomorphic but not equal.

        2 replies 0 retweets 3 likes
      4. benzrf (!!!)‏ @benzrf Jun 29
        Replying to @TheMichaelBurge @noop_noob @ModelOfTheory

        that makes no sense... first of all, disjoint union is also only commutative up to isomorphism; second of all, you're only saying that disjoint union is commutative, which is exactly what OP says about *multiplication*

        1 reply 0 retweets 0 likes
      5. Michael Burge‏ @TheMichaelBurge Jun 29
        Replying to @benzrf @noop_noob @ModelOfTheory

        Sorry, I meant "union of disjoint sets" not "disjoint union". Multiplication of sets is not commutative. Multiplication of set equivalence classes is.

        1 reply 0 retweets 0 likes
      6. benzrf (!!!)‏ @benzrf Jun 29
        Replying to @TheMichaelBurge @noop_noob @ModelOfTheory

        ok, but nonetheless, you're only saying that addition is commutative and multiplication is commutative up to a weaker equivalence. that doesn't really correspond to the tweet.

        1 reply 0 retweets 0 likes
      7. Michael Burge‏ @TheMichaelBurge Jun 29
        Replying to @benzrf @noop_noob @ModelOfTheory

        Commutative ⊨ Unordered ~Commutative ⊨ Ordered

        1 reply 0 retweets 0 likes
      8. benzrf (!!!)‏ @benzrf Jun 29
        Replying to @TheMichaelBurge @noop_noob @ModelOfTheory

        like i said, though, that doesnt make sense when the original tweet literally said "commutative" for that matter, it also said "numbers", not "sets", and if you wanna argue that it meant ordinal or cardinal numbers, well, those are already considered up to a weaker equivalence

        1 reply 0 retweets 0 likes
      9. Michael Burge‏ @TheMichaelBurge Jun 29
        Replying to @benzrf @noop_noob @ModelOfTheory

        The original tweet is incorrect under a strict reading. The principle of explosion allows no insights to be gained from an incorrect statement. Happy?

        1 reply 0 retweets 2 likes
      10. 1 more reply
      1. Jake Januzelli‏ @Januzellij Jun 29
        Replying to @ModelOfTheory

        Why is this not an artifact of a definition? Afraid I don’t get the point

        0 replies 0 retweets 0 likes
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