# Excluding interval from N

I've recently been learning factorials in school. If there is an equation (in $\mathbb N$) with $(n-5)!$, I have to ensure that $n$ is not 1, 2, 3 or 4. I've been told that I should write domain:

$D = \mathbb N \setminus \{1; 2; 3; 4\}$

My question: Is it possible to use an interval? Can I write

$D = \mathbb N\ \setminus \langle1; 4\rangle$ (or for someone more common $[1; 4]$)

? And if not, is there another "solution"? Exclude 4 numbers is easy but what if there were 50?

Thanks

• Not sure this is clear. Are you asking: "is there a simple expression for the product $5\times 6 \times \dots \times N$"? – lulu Mar 7 '16 at 19:21
• Have a look at this question, math.stackexchange.com/questions/430851/notation-for-intervals the second part of the first answer refers though to a French notation – Stravog Mar 7 '16 at 19:23
• $\mathbb{N} \setminus [1, 4]$ should make sense; both $\mathbb{N}$ and $[1, 4]$ are sets, set difference is well-defined here. – DylanSp Mar 7 '16 at 19:25
• @DylanSp Yeah that is my point, we french are used to write it with double braces – Stravog Mar 7 '16 at 19:26
• @Stravog Thanks. I'm from Czech Republic and I'm used to write $\langle1;4\rangle$ but what I've read over questions here, $[1;4]$ is more common.. – Martin Heralecký Mar 7 '16 at 19:29

## 2 Answers

You can write $\mathbb{N} _{\geq5}$ as well.

I would not use "interval notation" here. [1, 4] would normally be interpreted as the set of all real numbers between 1 and 4 which is not what you intend. Instead, use {1, 2, 3, 4}. For a more general situation, such as "all integers between 1 and 50" or "all integers between 1 and n", use {1, 2, ..., 49, 50} and {1, 2, ..., n-1, n}, respectively.

• Every teacher I had told me to avoid using any $...$ – Stravog Mar 7 '16 at 19:40