Writing a half-ray as a countable union

Question

I was trying to prove that monotone increasing functions are Borel measurable and I came across a step where I had to write $[x_0, \infty)$ as a countable union, I suggested either $\bigcup_{n=1}^\infty [x_0,n)$ or $\bigcup_{n=1}^\infty [x_0, n]$. I am unsure which one to choose however, are both right?