TITLE: How to write a set with an index
QUESTION [7 upvotes]: I'd like to write a set $\{x_1, x_2, ..., x_n\}$ in a simple way.
What is a popular way?
In my high school, I wrote it as $\{x_i\}_{i=1}^{n}$. Is it a correct way?

REPLY [4 votes]: in the set theory we have  $\{x_1,...,x_n\}=\{x_i\mid 1\leq i\leq
n\}=\cup_{1\leq i\leq n}\{x_i\}$  so is the set of $n$ elements,
and the set
$\{x_i\}^{n}_{i=1}=\{x_1\}\{x_2\}\cdot\cdot\cdot\{x_n\}=\{(x_1,\cdot\cdot\cdot
x_n)\}$ is a set of one element.