Given that $x \in R:$
$$[x,\rightarrow ) := \{y \in R\ | \ y \ge x \} = \bigcup \{[x, x + n) \ | \ n \in N\} $$
What I don't understand here is why the right equality holds (from which will follow that $[x,\rightarrow )$ is open)? Could you please point me to a proof of this fact.