how mathematicians “prove” that mathematical proofs, such as the Pythagorean Theorem, are true for any input?

Question

how mathematicians “prove” that mathematical proofs, such as the Pythagorean Theorem, are true for any input?

In: 51

Answer 1

They prove it by showing what rules don’t say, but that rules still mean. For example, if balloons aren’t allowed in the house, we can also say balloons aren’t allowed in the living room. The rules don’t say balloons aren’t allowed in the living room, but since the living room is in the house, we can prove that balloons also aren’t allowed in the living room.