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
> For any number n, where n is a prime >2, the sum of the factors of n cannot be odd
Adding things together.
All prime numbers have exactly 2 factors: 1 and itself.
An even number has 2 as a factor.
Assume a prime number >2 that’s even. It must have the following factors: 1, n, 2 and n/2. This is impossible because prime numbers by definition only have 2 factors. Therefor the assumption is wrong, all prime numbers n>2 are odd. This is proof by assuming the opposite and proving it false (this only works when there’s only 2 options).
The prime number n>2 is odd. We just proved that. Any odd number + 1 is even. QED.
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