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
A rational number can by definition be expressed as the fraction of two integers p/q where q is not zero. Any decimal section that terminates or starts to repeat will be possible to express with p and q as integers. Proof that a number is irrational tends to be to show it is impossible to express at the fraction of two integers
There are many proofs pi is irrational none of them are simple enough to write here on Reddit but look at [https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational](https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational) with 6 different proofs.
There are proof for the square root of 2 too [https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality](https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational) you can show that any square root that is not an integer is irrational
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