It’s not 10?
Also, oh God, I got yours as I was typing.
concat: “11”
cat: ignores your inquiry
I love the comment that it’s “occasionally useful”
+ 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).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."
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.
Nah not anymore, now you spend a day or so building some convoluted excel calculator once so that you never need to do the calcs again.
Then, 3 years later when you go to add or change something in that calculator, you have absolutely no idea how it works and decide the change wasn’t that important anyway.
Yeah, define “zero”.
The one invented on India at around the Middle Age is a different one. The one you are asking about is very old.
You forgot accountant
“What do you need it to be?”
How old this be inductive reasoning?
Surely the philosopher is the one looking for definitions…