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

There is also ‘proof by contradiction’ where you start off by assuming that the thing you want to prove is NOT true.

For example, √ 2 is an irrational number. To prove this by contradiction assume that it is rational, i.e. it equals a/b then there are a series of logical steps that ultimately show that a contradiction occurs, for example that ‘a’ is both odd and even.

Using the same argument it is possible to show that √ n is an irrational whenever n is not a square number.