this post was submitted on 22 Jul 2024
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Science Memes

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submitted 3 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
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[–] Wilzax@lemmy.world 12 points 3 months ago (8 children)

Now define "+"

[–] MBM@lemmings.world 8 points 3 months ago (3 children)

+ 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.

[–] funkless_eck@sh.itjust.works 4 points 3 months ago (1 children)

seems a little sus to use + to define +

[–] apolo399@lemmy.world 9 points 3 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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