But like… what does the proof even entail? I feel if you asked a child (or maybe me) what the proof was they’d say “well the definition of those two numbers, and the definition of plus means that 1+1=2”. What else is there?
Proving it from the definition is quite easy. The hard part is to build up all the concepts that you need to define the numbers and the operation in the first place. What exactly that entails depends on what axiom system and system of logic you are using. For example, here is the Metamath proof of 1 + 1 = 2, where you can click to see all the axioms, definitions and theorems involved.
But like… what does the proof even entail? I feel if you asked a child (or maybe me) what the proof was they’d say “well the definition of those two numbers, and the definition of plus means that 1+1=2”. What else is there?
Proving it from the definition is quite easy. The hard part is to build up all the concepts that you need to define the numbers and the operation in the first place. What exactly that entails depends on what axiom system and system of logic you are using. For example, here is the Metamath proof of 1 + 1 = 2, where you can click to see all the axioms, definitions and theorems involved.
I don’t even know where to start with that page. I feel like the curtain has really been pulled back today!