# About Math notation: the set of the $n^{th}$ natural numbers

It’s true that I can write the set of the $n^{th}$ natural number as $[ n]$?

For example, $[10]= \{1,2,3,4,5,6,7,8,9,10 \}$. And in which math contex this is use?

#### Solutions Collecting From Web of "About Math notation: the set of the $n^{th}$ natural numbers"

You can define $[n]$ however you want, so it can be true. Despite that, it is a common notation for the set $\{k\in \mathbb{N} : k\leq n\}$, yes.

This notation is used more often on Elementary Set Theory and Discrete Mathematics. Unfortunately analysts don’t use it much. I’ve never seen it being used in Abstract Algebra or Linear Algebra either.