# Is the sentence "For every integer 3<k<15 " written correctly?

In my mathematics paper, I wrote：

``````For 3<k<15, ... .
``````

I later discovered that k needs to be emphasised as an integer. So I wrote this:

``````For every integer 3<k<15, ... .
``````

I'm not sure if above sentence is normal. I frequently encounter the following sentence.

``````For every integer k>3, ... .
``````

Note that k is close to the word “integer”.

So I would like to ask if the above write up is correct. I've also tried writing like this, but I'm also not sure if it's the norm.

`````` For every integer k with 3<k<15, ... .
``````
• Is n an integer, a real, or what? Should we consider every possible n that is greater than sin(k), or do you just assert that there exists some n that is greater than sin(k), or what? Jul 21, 2022 at 2:27
• This quetion would probably get better answers on one of the math stackexchange sites, where they could also share how to express this in mathematical notation. Jul 21, 2022 at 2:28
• @ThePhoton Thanks. We don't care whether n is real (integer) or not. Jul 21, 2022 at 2:29
• That's not English, it's Mathlish. Jul 21, 2022 at 2:49
• Another alternative would be "for k = 4, ..., 14", every mathematician would understand from this that k is an integer. Jun 16, 2023 at 9:50