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
There are many strategies to proof, but they all rely on making some basic assumptions and definitions of things and showing how facts following from them always lead to a particular conclusion.
If n is a prime >2, then it has 2 factors {n, 1}. If it had other factors it would not be prime.
All primes other than 2 are odd because a hypothetical even prime would be of the form 2k where k is an integer (this is basically the definition of an even number) and would thus have 2 as a factor.
The sum of an odd number (2k+1) and 1 is even because 2k+2 has 2 as a factor.
As such, the sum of the factors of primes > 2 is even.
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