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.
A prime number n by definition a number that can’t be formed by multiplying any smaller number together. The only factors you can have is the trivial 1*n.
A even number is n=2k where k is a integer.
A odd number is n=2k+1 where k is a integer.
If a prime number is even it can be written as 2k. So all even number have the factor 2. Because a prime number only can have the factor 1 and itself the only even prime is 2
So both factors of a prime number n >2 are odd
So the sum of the factor of a prime number >2 can be written as 1+(2k+1)= 2k+2 =2(k+1) and that is a even number. So the sum of the factor of a prime number is a even number.
For more and better example look at [https://en.wikipedia.org/wiki/Mathematical_proof](https://en.wikipedia.org/wiki/Mathematical_proof)
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