im just wondering since irrational numbers supposedly dont end and dont repeat either, why is it not a possibility that after a huge bunch of numbers they all start over again or are only a single repeating digit.
In: Mathematics
There are a few different methods of proofs in Mathematics. The one people are referencing in the first couple of responses (for proving √2 is irrational) is a Proof by Contradiction. For that proof you start with an assumption (often the opposite of what you are trying to prove). Then you go through steps until you reach a contradiction. In the case of the √2 proof, it is that your reduced fraction of a/b is not reduced.
Once you get the contradiction, your assumption must be wrong. And since your assumption is binary (it is only one of two options), the opposite of your assumption must be correct.
The same type of proof is used to prove there are an infinite number of prime numbers.
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