How do we know irrational numbers don’t repeat?
In: Mathematics
Well that’s their definition… rational numbers repeat (or just stop), irrational numbers do not. More specifically a rational number can be written as a fraction where the top and bottom are both whole numbers, irrational numbers can’t do that.
Maybe you mean, “How do we know number X is irrational?”, like the square root of 2, or Pi, or e. These are questions answered here already. Generally you prove that a fraction of whole numbers is somehow impossible and that’s good enough.
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