How do we know irrational numbers don’t repeat?
In: Mathematics
A number is rational if it is the ratio of two integers. It is irrational if it can’t be written as such.
Let’s say you have a number that does repeat. For example x=0.123123123…
So 1000x = 123.123123123…
Subtract x from both sides and you get 999x = 123, or x = 123/999, i.e. x is rational.
Therefore if x is repeating then it is rational.
There’s another proof that shows that if x is rational then it is repeating (or finite).
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