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 basically work this way:
1. Say something you know is true.
2. Then, say the same thing, but slightly differently. It must still be true.
3. So, whatever you come towards in the end must also be true.
Let’s see an example. I will postulate that x + (-x) < 1.
Let’s start by saying something we know to be true:
1. 1 – 1 = 0
2. Let’s multiply by x:
3. 1(x) – 1(x) = 0
4. Now, we also know that 0 < 1. So if x < 0, x < 1!
5. So, 1 – 1 < 1.
6. But, then, also 1(x) – 1(x) < 1.
Really ,we never actually said anything new at any point. We stated something we knew was true, and kept reformulating it until we got what we wanted.
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