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[-] MBM@lemmings.world 8 points 3 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.

[-] funkless_eck@sh.itjust.works 4 points 3 months ago

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.

this post was submitted on 22 Jul 2024
403 points (94.7% liked)

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