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(Note. I deleted the previous question as the discussion was focusing too much on the math.)

I am writing a research paper in mathematical analysis and I have a situation in which I want to give a name to some mathematical object. I was thinking to use the adjective "slack" (meaning "loose" "with untied ends" referred for instance to a piece of rope).

Below a stupid (made up) example to help clarify the way I would use such a word:

Definition. A slack number is an odd integer number that is a multiple of 3.

Example. The number 9 is a slack number.

Of course the mathematical objects I will refer to are different with respect to the ones above and you can trust me it makes sense to use an adjective with that meaning (or, say, I will ask on MathStackExchange in case I have doubts on that).

My question. I would like to know whether the word "slack" could have some different meanings (vulgar, sexual, slang,...) or other reasons which could make it inappropriate for academic writing (too colloquial, etc.).

Remarks.

  • Any remarks would be appreciated.
  • The word might look random, but I think it fits reasonably well in what I am doing.
  • I know the adjective has other meanings (negligent, careless...), but I am confident the right interpretation would be clear from the context.
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    Hello, Lorenzo. ELU deals with standard usages, for instance existing definitions and etymology, that can be researched. Requests for comments on suitability of new stipulative definitions are almost certainly off-topic as too open to opinion, but I will say that a quick Google search for "slack number" leads to an existing use of 'slack' in slack time [Kate Eby at SmartSheet)].
    – Edwin Ashworth
    Commented Dec 8, 2022 at 19:12
  • @EdwinAshworth thank you for your comment. My question is not on the suitability of my definition in a mathematical framework, but rather on the common uses of the word "slack" and whether it could be too colloquial or vulgar for an academic writing. I wrote the above definition just to give an example on how I would use the word in a paper. But I could be misunderstanding your comment
    – Lorenzo Pompili
    Commented Dec 8, 2022 at 19:32
  • I'm saying that 'slack' already has a usage in the maths (business maths) domain, and quite a few others; proliferation of senses especially intradomain is far from ideal. But whether this should deter you from redefining 'slack' in 'slack number' is not overall an issue for ELU, as opinions will differ (... reasons which could make it inappropriate for academic writing). In such cases, we usually advise enquirers to check on their supervisors' opinions. They're pro tem the boss.
    – Edwin Ashworth
    Commented Dec 9, 2022 at 15:22

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My question. I would like to know whether the word "slack" could have some different meanings (vulgar, sexual, slang,...) or other reasons which could make it inappropriate for academic writing (too colloquial, etc.).

The English language is dominated by context. It is the context that makes a word vulgar:

"Get that bloody cat off me!" can be vulgar if "bloody" is taken to be an emphatic, but perfectly acceptable it the cat is bleeding.

Your use of "slack" will be in context. In context, it will not be objectionable.

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  • (Sorry, I didn't read the last line of your answer). Thank you for your answer and also for your comment on my previous question. I will try to be sure about the context before using that word then
    – Lorenzo Pompili
    Commented Dec 8, 2022 at 19:48
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The main adjectival usages of slack are summarised (for example) in the Cambridge dictionary:

Cambridge
not tight; loose:
showing little activity; not busy or happening in a positive way
something that is slack is not strict or effective enough

This (and my own long experience of English) suggests that slack does not have unpleasant or obscene overtones and therefore could be used with confidence to qualify a number.

There are many precedents for this. You as a mathematician will know them: we have magic numbers, perfect numbers, imaginary numbers, rational numbers and irrational numbers. You are therefore well justified in introducing the concept of a slack number, so long as you define it unequivocally.

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