Math is fascinating to me, though I struggled with math in high school and only took the minimum I needed. (Age changes things, man.) I’m reading a book on Wiles’ proof for Fermat’s Last Theorem and got curious about proofs.
At what point does something move from an assumption with examples (well yeah. Look at this) to a full proof?
Simple example that came to mind:
For any number n, where n is a prime >2, the sum of the factors of n cannot be odd.
In: Mathematics
Proofs aren’t really about examples and assumptions. We might start a proof with an assumption, but that’s not the proof – that’s the statement we’re trying to prove. And if we give an example, that’s not a proof either, until we can show that it’s true for every example you can imagine. If I show you a hundred examples of something and say “See? That’s proof that it’s true,” all I’ve proved it that it’s true for those hundred examples. You only need to show me *one* example where it’s not true to show I’m wrong.
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