Excluding interval from N

Question

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

Answer 1

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.

Answer 2

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