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I wrote in my manuscript: 'Let f be a k-face of D where $k \ge 4$.'

However, I feel that replacing 'where' with 'with' might be more appropriate. I'm a bit uncertain, so I'm posing this question. Can both be used, or is there a strict distinction between the two?

P.S.: Unlike the math SE and some others, this site appears not to support LaTeX; please note that $k \ge 4$ indicates that k is greater than or equal to 4.

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    "Let f be a k-face of D where k ≥ 4"
    – Henry
    Nov 29, 2023 at 9:50
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    This is a matter of style. I suspect both convey a similar meaning and will be understood.
    – Henry
    Nov 29, 2023 at 9:52
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    I’m voting to close this question because math has its own formats. Nov 29, 2023 at 14:07
  • @YosefBaskin Are you referring to LaTeX, or are you talking about English styles? The focus here is not on LaTeX.
    – licheng
    Nov 29, 2023 at 14:10
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    The question is not a matter of proper English, but what is standard in technical formulas. This site doesn't handle those issues. Nov 29, 2023 at 14:14

1 Answer 1

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Either where or with is fine in your sentence, as would be for. Here the function of the prepositional phrase is merely to restrict the values that k may take, and that restriction applies in the definition of f. Indeed, k is introduced merely to serve in defining f.

A context in which there would be a preference among these three prepositions is in phrases that explain variables’ semantics, which conventionally use where. Thus,

The more general form of Newton’s second law of motion, the form that must be used to obtain the force F involved in changing the motion of a body of non-constant mass, is

F = dp/dt,

where the vector p is the body’s momentum.

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