Coverage actually means inclusion. For example, (1/n, 2/n)(n= 1, 2,3, ...) is the open cover of (0, 1), which means any real number x in (0, 1). X<2/n. This is easy to prove. But this coverage is not finite, because for any finite value n, it can be proved that there must be a number in (0, 1) (such as1(2 * n)), so this number is not (11,2/ 1). This is why we say that (1/n, 2/n)(n= 1, 2,3, ...) is an open covering of (0, 1), but there is no finite sub-covering.