How so? Even a real interval of a finite length cannot be covered by any set of intervals of a smaller total length. (Unless the person you are trying to explain this to starts raising questions about the meaning of 'interval' or 'length', in which case the meaning of the original question becomes just as uncertain in the first place.)

> Even a real interval of a finite length cannot be covered by any set of intervals of a smaller total length.

You’ve only restated the problem without saying _why_ covering the reals is different.

Because the 'intervals' in question are already 'real'?