Comment on 1 + 1

FiskFisk33@startrek.website ⁨11⁩ ⁨months⁩ ago

• Wilzax@lemmy.world ⁨11⁩ ⁨months⁩ ago

  Now define “+”

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  • FiskFisk33@startrek.website ⁨11⁩ ⁨months⁩ ago

    Image

    I love the comment that it’s “occasionally useful”

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    • Wilzax@lemmy.world ⁨11⁩ ⁨months⁩ ago

      Hmm yes… set theory… I don’t understand anything happening here

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      • FiskFisk33@startrek.website ⁨11⁩ ⁨months⁩ ago

        There is actually a really good explanation for us curious non-mathematicians here:
        blog.plover.com/math/PM.html

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  • MBM@lemmings.world ⁨11⁩ ⁨months⁩ ago

    + is a map from N×N to N where a + 0 = a and a + S(b) = S(a + b) (S is the successor function that gives the next number).
    Then 1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2.

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    • funkless_eck@sh.itjust.works ⁨11⁩ ⁨months⁩ ago

      seems a little sus to use + to define +

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      • apolo399@lemmy.world ⁨11⁩ ⁨months⁩ ago

        No, it’s correct. You define the operation by it’s properties. It’s not saying that “a plus 0 = a” but "the result of applying the binary operation ‘+’ to any number with 0 should give the original number."

        • is just a symbol. You could instead write it as +(a,0)=a and +(a,S(b))=S(+(a,b)).

        You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.

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• porl@lemmy.world ⁨11⁩ ⁨months⁩ ago

  I really recommend the YouTube channel “Another Roof”. His first few videos were building up exactly this idea, as well as building up all the real numbers (possibly complex too if I’m remembering correctly). Sounds like a dry topic but he uses humour really well throughout. youtube.com/@anotherroof

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  • FiskFisk33@startrek.website ⁨11⁩ ⁨months⁩ ago

    ooh, that looks interesting!

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