How to read "$\bigcup_{n = 1}^\infty$", as in $\bigcup_{n = 1}^\infty[2n, 2n+1]$ So I am given an equation such as this:
$$
T = \bigcup_{n = 1}^\infty[2n, 2n+1]
$$
And I am meant to find the infimum and supremum of the set however I was never taught how to read what this mathematical notation is saying? What will the set look like?
 A: when $n=1, [2n, 2n+1]=[2,3]$
when $n=2, [2n, 2n+1]=[4,5]$
when $n=3,[2n, 2n+1]=[6,7]$
and et cetera.
$T$ is the union of closed intervals of length $1$, where the left boundary is an even number that is at least $2$.
In general $$\bigcup_i A_i = \{ x: \exists i, x \in A_i\}$$
A: The small numbers above and below the $\bigcup$ tells you what different values of $n$ we consider, and for each $n$ whatever is on the right of the symbol becomes a different set. So you have the collection
$$
\underbrace{[2, 3]}_{n = 1}, \underbrace{[4, 5]}_{n = 2}, \underbrace{[6, 7]}_{n = 3},\ldots
$$
And then the symbol $\bigcup$ itself tells you that you combine them using the union operation ($\bigcup$ is a large $\cup$, after all). There is a corresponding notation $\bigcap$ for intersections.
Compare this to something like
$$
\sum_{n = 1}^\infty \frac1{n^2}
$$
where the small numbers above and below $\sum$, as well as the expression to the right of $\sum$, together tells you that you have the set
$$
\underbrace{\frac11}_{n = 1}, \underbrace{\frac14}_{n = 2}, \underbrace{\frac19}_{n = 3}, \ldots
$$
of numbers, and then the symbol $\sum$ itself tells you what you should do with them (namely add them).
A: It indicates the union of all the closed intervals of the kind $[2n,2n+1]$ with $n\in \mathbb{N}$, that is
$$[2,3]\cup[4,5]\cup...\cup[2n,2n+1]\cup...$$
from here you can easily deduce infimum and supremum.
