How do you place text underneath and over an operator simultaneously?

Question

So as know, $\underset{i = 1}{\bigcup}$ is how you place text under an operator.

And $\overset{n}{\bigcup}$ is how you place text over an operator.

But how do you combine the two? I've tried things like \underset\overset{i=1}{n} \bigcup as well as $\underset{i=1}\overset{n} \bigcup$ but those are syntactically incorrect.

Main question: Basically, I want a union symbol with its initial index as i=1 and its ending index as n

Answer 1

You wrote,

So as know, $\underset{i = 1}{\bigcup}$ is how you place text under an operator. And $\overset{n}{\bigcup}$ is how you place text over an operator. But how do you combine the two?

\bigcup and \bigcap are defined as variable-sized math operators. This is, incidentally, also the case for \sum, \prod, and \int. Hence, placing subscripts and superscripts is no different than for \sum, \prod, and \int.

\documentclass{article}
\begin{document}
$\displaystyle\bigcup_{i=1}^n$ \quad $\bigcup\limits_{i=1}^n$ \quad $\bigcup_{i=1}^n$
$\displaystyle\bigcap_{j=1}^M$ \quad $\bigcap\limits_{j=1}^M$ \quad $\bigcap_{j=1}^M$
$\displaystyle\sum_{k=1}^K$    \quad $\sum\limits_{k=1}^K$    \quad $\sum_{k=1}^K$
\end{document}

Answer 2

Hope you are looking for \smashoperator from the package mathtools and the MWE is:

\documentclass{book}
\usepackage{mathtools}
\begin{document}
\[
\smashoperator[l]{\mathop{=}_{sub}^{sub}}
\]
\end{document}