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Real - or even rational - numbers are infinitely dense. What this means is that there is no real number immediately before any other since it is always possible to find another number which is better qualified to claim that position.

For example, 1/5 is less than 1/2 but is it "before"?

No, because (1/5 + 1/2)/2 = 7/20 is also less than 1/2 and is nearer. Is it "before"?

No, because (7/20 + 1/2)/2 is less than 1/2 and is nearer.

And so on.

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9y ago

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