# Set theory list all possible elements?

I just started learning set theory.I have a question I need to answer for revision. I missed a bit of my lecture so i'm a little lost and I have yet to receive my textbook.

The question is: "Write [–3..1] as a set by explicitly listing all its elements. "

Just wondering how that works?

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My gut reaction would be that this is impossible because $[-3,1]$ represents the set of all real numbers $x$ such that $-3\leq x\leq 1$. The fact that you are asked to do it, though, suggests to me that this is some special notation introduced in your course, possibly the set of all integers between $-3$ and $1$. If so, I would point out that I would "explicitly list" the set $[5..8]$ like so: $\{5,6,7,8\}$. –  Arturo Magidin Aug 17 '11 at 21:03
Thanks, I'll have to ask the professor. :) –  jojoi Aug 17 '11 at 21:17
@Arturo: $\{x\in\mathbb R\mid -3\le x\le 1\}$ is not explicit, I take it? –  Asaf Karagila Aug 17 '11 at 22:24
@Arturo Magidin: Note that the OP wrote $[-3..1]$, not $[-3,1]$. –  Ben Crowell Aug 18 '11 at 2:22
@Asaf: It's not a way of "explicitly listing all the elements", no. –  Arturo Magidin Aug 18 '11 at 3:11

If $n$ and $m$ are integers with $n\le m$, the two-dots notation $[n..m]$ commonly denotes the set of integers between $n$ and $m$ inclusive: $[n..m] = \{k \in \mathbb{Z}:n \le k \le m\}$. If that’s the convention that your class is using $-$ and it’s common in computer science, so it’s not unusual in discrete math courses $-$ then $[-3..1] = \{-3,-2,-1,0,1\}$.