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Here is a little puzzle I have been wondering about. I can't solve it, perhaps you can help.

We know there are infinitely many real numbers on the number line. Indeed, already between 0 and 1 there are infinitely many real numbers. So if a real number is a point on the number line, there must be infinitely many points between 0 and 1. This is only possible if the points have zero extension. Now, infinity times zero is still zero. So the number line must have zero length! This is obviously absurd. But where is the false premiss?

Source: Yanofsky, The Outer Limits of Reason.