Ways to Write Out Sets

Fun Class Activity:

1. List all the elements of the set $S = \{2n\ |\ 0 \le n \le 5\}$. Assume that $n$ is a non-negative integer.
2. Express the set $S = \{2n\ |\ 0 \le n \le 5\}$ using the ellipsis notation.
3. Express the set $\mathbb{Z}$ in set rule notation.
4. Express the set $\mathbb{Z}$ using the ellipsis notation.

Fun facts: The 'less than or equal to' symbol, or $\le$, is written in $\LaTeX$ as

$\le$

, and the 'greater than or equal to' symbol, or $\ge$, is written in $\LaTeX$ as

$\ge$

.

So $S = \{2n\ |\ 0 \le n \le 5\}$ is written as

$S = \{2n\ |\ 0 \le n \le 5\}$

.

The spaces that we add around the $|$ symbol (

$\ |\ $

) prevent the notation from being squashed, as in $S = \{2n | 0 \le n \le 5\}$ and

$S = \{2n | 0 \le n \le 5\}$

.