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
It’s such a failure of our system of math education that people tend to associate irrational numbers with their decimal notation being infinite and non-periodic. Decimal notation is, well, just a notation — whereas the basic, way more natural definition of irrational numbers is that they can’t be expressed as a ratio of two integers.
This doesn’t make it much easier to prove irrationality of pi in a Reddit comment, but it’s the starting point for the sqrt(2) proof which other commenters have kindly provided.
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