How is it proven that √2 or π are irrational? couldnt they just start repeating a zero after the quintillionth digit forever? or maybe repeat the whole number sequence again after quintillion digits

Question

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

Answer 1

I can’t explain it better than Taylor Swift does:

[https://www.youtube.com/watch?v=meudJkjKEe8](https://www.youtube.com/watch?v=meudJkjKEe8)