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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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There are lots of numbers less than one half. However, with fractions or real numbers you don't have an ordering, as you have with the whole numbers. Or rather, no NATURAL ordering. This is because, if you find a number that is close to one-half (for example), and less than it, you can always find another one that is even closer!

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Q: What is before one half?
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