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
math proofs at its simplest are just you take known assumptions, and manipulate them to show a result.
so we know integers are prime. and we know primes only have two factors, itself and one.
if we add one to an odd number, it’ll be even. if we add one to an even number, it’ll be odd. However, the only even prime is two, because any other numbers that are even are divisible by two (the definition of even numbers) so we know that all primes that aren’t two are odd. since they’re odd, if we add one, the only other factor of a prime, its even.
boom! We’ve proved it.
We however can’t prove things with examples. i can’t think of examples but even if something is true for the first 100000000000000000 numbers, it might not be true for the first 200000000000000000 numbers
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