Writing an interval with infinite unions or infinite intersection

Question

I don't know how to write intervals the infinite union or intersection, there are an $\it{IDEA}$ that I don't catch up.

For $a,b\in\mathbb{R}$,which is correct from this expression below and why:

$]a,b[=\bigcap_{n\in\mathbb{N}}]a+1/n,b-1/n[$

or $[a,b]=\bigcap_{n\in\mathbb{N}}]a+1/n,b-1/n[$

or $[a,b]=\bigcup_{n\in\mathbb{N}}]a+1/n,b-1/n[$

or $]a,b[=\bigcup_{n\in\mathbb{N}}[a+1/n,b-1/n]$

In general if we have an interval (for example $]a,\infty[$) and we want to express it whith other type of intervals using unions and intersections what is the methodology?

Answer 1

The first two are wrong since (a+1,b-1) is the smallest interval thus defining the intersection. The third is wrong since a and b are not members of any of the sets forming the union. The fourth is correct since all points (x) $a<x<b$ are included.

Note: I assume my comment about notation above is correct.