1
$\begingroup$

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

$\endgroup$
  • 1
    $\begingroup$ Not sure this is clear. Are you asking: "is there a simple expression for the product $5\times 6 \times \dots \times N$"? $\endgroup$ – lulu Mar 7 '16 at 19:21
  • 1
    $\begingroup$ 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 $\endgroup$ – Stravog Mar 7 '16 at 19:23
  • 1
    $\begingroup$ $\mathbb{N} \setminus [1, 4]$ should make sense; both $\mathbb{N}$ and $[1, 4]$ are sets, set difference is well-defined here. $\endgroup$ – DylanSp Mar 7 '16 at 19:25
  • $\begingroup$ @DylanSp Yeah that is my point, we french are used to write it with double braces $\endgroup$ – Stravog Mar 7 '16 at 19:26
  • $\begingroup$ @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.. $\endgroup$ – Martin Heralecký Mar 7 '16 at 19:29
3
$\begingroup$

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

$\endgroup$
2
$\begingroup$

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.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.