+ 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.
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.
Now define “+”
I love the comment that it’s “occasionally useful”
Hmm yes… set theory… I don’t understand anything happening here
There is actually a really good explanation for us math-curious non-mathematicians here:
https://blog.plover.com/math/PM.html
That’s some good read, thank you so much.
+is a map fromN×NtoNwherea + 0 = aanda + S(b) = S(a + b)(Sis the successor function that gives the next number).Then
1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2.seems a little sus to use + to define +
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.”
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.
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