this post was submitted on 22 Jul 2024
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Science Memes

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submitted 4 months ago by [email protected] to c/[email protected]
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[–] Wilzax 12 points 4 months ago (2 children)

Now define "+"

[–] [email protected] 32 points 4 months ago (1 children)

I love the comment that it's "occasionally useful"

[–] Wilzax 15 points 4 months ago (1 children)

Hmm yes.. set theory... I don't understand anything happening here

[–] [email protected] 12 points 4 months ago* (last edited 4 months ago) (1 children)

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

[–] [email protected] 3 points 4 months ago

That's some good read, thank you so much.

[–] [email protected] 8 points 4 months ago (2 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.

[–] [email protected] 4 points 4 months ago (1 children)

seems a little sus to use + to define +

[–] apolo399 9 points 4 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.