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?
    – The Photon
    Commented Jul 21, 2022 at 2:27
  • 4
    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.
    – The Photon
    Commented Jul 21, 2022 at 2:28
  • 2
    That's not English, it's Mathlish.
    – Hot Licks
    Commented Jul 21, 2022 at 2:49
  • 1
    Another alternative would be "for k = 4, ..., 14", every mathematician would understand from this that k is an integer.
    – J.J. Green
    Commented Jun 16, 2023 at 9:50
  • 2
    I’m voting to close this question because it's about mathematical formatting, too specialised for ELU. Commented Jun 3 at 22:11

3 Answers 3


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).

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