Take any arbitrary . There is a collection of intervals so that
and the sum of their length never exceeds .
To see this, for any , take any positive sequence converging to . For example, will do. Since rational numbers are countably many, we can cover every rational number with open interval centered at with .
This is used to show that rational numbers, in the universe of real numbers, have measure zero, since we can control how small our is going to be.