Borel sets. Need to prove.

Question

I need to prove that set $(1,4)$ is Borel set. Actually, I have no idea how to do it. I was looking for theory. And find something.

Let $I={(1,4), a<b, \text{ and } a,b \in R}$ Than $(1,4)= \cup_{n=1}^\infty (1, 4-\frac{1}{n}], a<b$.

and it is a proof? How I should prove it?

Answer 1

The Borel sets in $ \mathbb R$ are generated by the open sets in $ \mathbb R$ and $(1,4)$ is open !