how mathematicians “prove” that mathematical proofs, such as the Pythagorean Theorem, are true for any input?
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Proofs are a series of agreements you can make based on logic and previous agreements.
For example.
People should agree that A = A, and B = B. Silly as it is, its important because I’m about to start including B’s and A’s left and right.
If we agree on that then we might agree A + B = AB
We might also agree on how x and y are sorted out on a graph.
We can then also agree what a slope is, Go over A times, and up B times….we’re on to something.
I’m not going to go over the whole proof, but eventually we’ll find going over A and up B in a consistent way makes consistent patterns; patterns that are the Pythagorean theorem.
The wiki has many proofs by construction as well as formal proofs.
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