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When describing some experimental results, if two physical quantities (let's call them a and b) seem to depend on each other, it is often desirable to say what happened with one of them if the other went up or down, using the words increase and decrease. If, for example, a = b, then there may be several choices of the same phrase:

  1. We observed an increase in b with an increase in a.
  2. We observed an increase in b with increasing a.
  3. We observed increasing b with increasing a.

Personally, I tend to use the 1st version because both "increases" are nouns, which gives the sentence a semblance of self-consistency. However, thinking like that, two gerunds in 3rd would also make the sentence self-consistent. Besides, I cannot quite justify why the 2nd could be wrong.

The question is, which one of the example sentences is correct, and if more than one, then what are the differences between them (e.g. maybe there are situations when one should be preferred over the other).

  • Your command of English is excellent. All three wordings are correct and clear. At this point, I think all a good answer can give you is ideas for exploring and weighing the full range of possible wordings—how they differ in emphasis, how they follow or vary the most common formulations, etc. – Ben Kovitz Oct 30 at 22:34
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To my ear as a mathematician (and I can't find anything to back this up currently) in the forms you have described above:

Increase describes an amount. A increased by 6%, 5KG etc.

Increasing describes a trend or scale. A is increasing logarithmic-ally, in proportion to time etc.

I don't believe that either is incorrect, but I would certainly tweak the phrases depending on the context.

I.e.

We saw an increase in the population of rabbits with increasing time.

We saw a decrease in the population of rabbits with an increase in foxes.

We observed an increasing rate of growth for the rabbit population with increasing time.

Related but I don't think duplicate: On the increase vs increasing whats the difference between increased and increasing

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