Any open interval in R is union of intervals of the form (a,b] As part of a proof that the Borel Set $B\mathbb(R)$ is generated by the collection of subintervals of the reals of the form $(a,b]$, my measure theory textbook (Cohn) asserts that any open interval $(x,y)$ can be written as the union of a sequence of sets of the form $(a,b]$.
This seems intuitively true, but I'm stuck as to how one would formally prove that. Can anyone point me in the right direction?

Hint: Consider $\bigcup_{n\in\mathbb{N}}{(a,b-\frac{1}{n}]}$
