I want to write the following sentence:
The space O(X) (O(Y)) has functions defined on it as g(x)–f(x) (g(x)–f(x)).
By which I mean:
The space O(X) has functions defined on it as g(x)–f(x) and the space O(Y) has functions defined on it as g(x)–f(x).
But the parentheses are kind of distracting to read. What should I do about it?
@Buzz gives a good answer, highlighting that it is a style question for which people have different preferences. I personally don't like to use anything other than round parentheses, so my preferred approach to avoid the confusion is to use additional words as buffer:
The space O(X) (or, alternatively: O(Y)) has functions defined on it as g(x)–f(x) (alternatively: g(x)–f(x))...
As Federico Poloni points out, it is customary in mathematics writing to use "respectively", abbreviated as "resp.".
This gives, for your example:
The space O(X) (resp. O(Y)) has functions defined on it as g(x)–f(x) (resp. g(x)–f(x)).
Readers used to mathematical writing will have absolutely no issue with this sentence, and they will easily "skip" over the parenthesis without being distracted.
You can even "chain" them:
The space O(X) (resp. O(Y), O(Z)) has functions defined on it as g(x)–f(x) (resp. g(y)–f(y), g(z)-f(z)).
That being said, your sentence is weird (no Y / y in the second part of the sentence), since it seems that O(X) and O(Y) are defined the same way: do you mean
The space O(X) (resp. O(Y)) has functions defined on it as g(x)–f(x) (resp. g(y)–f(y)).
assuming that it is clear that x ∈ X and y ∈ Y?
This is a style question, so there is not going to be a uniform answer that everyone agrees on. Some people use (and some journals seem to prefer) nested parentheses just like in your examples. I personally find this both esthetically unappealing and often hard to parse.
My practice (and this seems to be followed by a fair number of journals in the mathematical sciences) is to use delimiters in running text the same way that I would in mathematical expressions. For a expression like the one given in the question,* that would mean
The space O(X) [O(Y)] has functions defined on it as g(x) – f(x) [g(x) – f(x)]....
I find that more readable than text that involves the same delimiter repeated (even if the text and math parentheses are in different fonts). Moreover, this continues with further delimiters in the pattern
{ [ ( { [ ( ) ] } ) ] }
so that, for example, if a parenthetical includes a mathematical expression with square brackets, it would be marked off with French brackets, e.g.
This is the largest the function can grow {assuming, as before, that Δ[sin(x)/x] remains within the unitarity domain}, so we can conclude...
*Actually, this expression, even with the square brackets has the potential to be confusing. As a general rule, in any situation where you are using multiple delimiters like this, it is good to look to see whether you can tweak what you have written to make it more readable. For example, I think your statement would be still easier to follow with the following added clarifications:
The space O(X) [respectively, O(Y)] has functions defined on it as g(x) – f(x) [respectively, g(x) – f(x)]....
(Maybe the second "respectively" is superfluous, but it probably doesn't hurt.)
Your example is weird, as people have said, because both have functions defined as g(x)–f(x). If this is really what you want (TBH it sounds as if you do not quite understand what you're trying to do) you could just say: spaces O(X) and O(Y) both have functions g(x)–f(x) defined on them.
More generally, it is better to write: the dah-dah has a dee-dee. Similarly, the pah-pah has a bee-bee rather than the dah-dah (pah-pah) has a dee-dee (bee-bee). I understand you aim to avoid boredom and annoyance on the part of the reader, but the extra verbiage is usually worth the clarity gained. Only when the reader is seeing all this for the umpteenth time, would I use the parentheses construction.
Putting respectively or or else: in the parentheses is helpful, but at that point your wordiness is about the same as the one at a time construction, so why bother?
In this simple example (and coming from a background in physics, where we can be a little lax with our mathematical language) I would use a construction like:
The space O(X) has functions defined on it as g(x)–f(x), and likewise for the space O(Y).
(I suspect you could omit the 2nd "the space"; you could certainly omit the "and")
This fits with my general approach of restructuring the sentence to avoid awkwardness. Of course this isn't always possible
