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Good one, yes. I think the way I expressed it is more easy to visualize, what do you think?
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Yours is more intuitive. If you've already setup whatever it is you need to about irrational slopes, this is probably more of a slam dunk.
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Thank you! And yes, indeed, hence my temptation to steal it :P
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good job. another way to say this is that there does not exist any continuous interval of real numbers $(a,b)$ with $b>a$ that doesn't contain a rational number within it.