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
What’s not been answered yet is the second part of the question.
If either number started repeating a zero after the quintillionth digit, then it would be expressible as a rational number.
3.1400000… is exactly 314/100, and for any such number written in our number system that stops after a certain number of digits, you can do this.
But we have already proven that neither number can be expressed as a rational fraction, and so we also know that pi and root(2) don’t start repeating a zero after the quintillionth digit.
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