> Bad: We offer a completely different formulation of CFA.
> Better: We offer a different formulation of CFA.
Getting rid of all adverbs (e.g. "vigorously stir the solution," "monotonically increasing function," "spontaneously combustible") hardly seems wise, whether technical writing or not.
I also disagree about the "beholder words"; to me "it was surprisingly low" means "I am drawing your attention to the fact that the low value surprised me" rather than "you need to be surprised by the low value".
my reasoning is that the former is more of a parenthetical, as much as to say "the results were low (and it surprised us)", rather than putting the "us" who were surprised front and centre and making the low results subordinate to that.
I agree with your interpretation, but here the issue is that "beholder words" don't give the reader the information necessary for them to make their own judgment. Readers are left thinking "ok, but how low is 'surprisingly low?'" Writers should tell the reader the exact number, saying "surprisingly" communicates nothing because it's relative.
If the function goes horizontal sometimes, then it is nondecreasing. If always, then it's constant (at least if continuous).
Much jargon works this narrowing way, to demarcate that the concept should not carry the everyday cluster of associations and meanings, but rather a domain-specific meaning.
Not at all. A function can be increasing over a given interval without that increase being monotonous.
The monotonically is important because it says that at every zoom level the function is increasing, while it being increasing just says it about the function shape in general.
Any function that decreases over any interval of its domain is not defined as an increasing function, rightly so.
A function that gets large with increasing independent variable can be called an asymptotically increasing function under the right conditions.