Show that each subset of R is not compact by describing an open cover for that has no finite subcover.

A) [1,3)

C) { 1/n : n in N}

What I dont understand is when my professor did a few examples of these, he would often, in for example [0, 1), write an infinite union of sets but would start it slightly less than 0?

For example for A would, $\displaystyle \cup^\infty$ (0, 3/n) work?