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

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? Commented 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. Commented Jul 21, 2022 at 2:28
• That's not English, it's Mathlish. Commented 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. Commented Jun 16, 2023 at 9:50
• I’m voting to close this question because it's about mathematical formatting, too specialised for ELU. Commented Jun 3 at 22:11

As one is reading it would help to specify k as the element of interest. Finding it hidden in 3<k<15 will make the average reader chortle with "Of course 3 is less than 15".

With that in mind I would use, "For every integer k where 3<k<15 we have the following claim;"

A good mathematician will not get lost but we generally write for the average reader.

It would be clearer if it were written

For every integer k, 4 ≤ k ≤ 14.

Since k is an integer, there's no reason to use the strict inequality sign, and it's somewhat confusing if you do.

For every integer 3<k<15, P(k).

Strictly speaking, there's a disconnect between the declaration and its object of interest, k: the statement seems to read as “For every integer 3 is smaller than k, which is smaller than 15,...”

Better (the final suggestion being the full logical expansion):

• For every k in {4,5,6,..., 14},  P(k).

• For every integer k that is strictly between 3 and 15,  P(k).

• For every integer k such that 3<k<15,  P(k). ✅

• For every integer k,  if 3<k<15, then P(k).

• For every k,  if k is an integer and 3<k<15, then P(k).