# How can I use parentheses when there are math parentheses inside?

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?

• Your sentence makes no sense to me. If you include the context (perhaps a paragraph) in which it appears we might be able to suggest wording. This question might be better asked on math.stackexchange. If you post there, delete here. Commented Jul 19, 2022 at 2:11
• Question on Writing SE as to whether such an expression is a good idea (featuring a detailed elaboration by me why it never is): Is elaborating the opposite case in brackets acceptable and clear? Commented Jul 19, 2022 at 8:08
• Also: Your particular definition is weird, as the second pair of alternatives is identical and none of the functions seem to be related to X or Y. Even if I ignore the last part, the symbol O is overloaded, such that I don’t think it is clear to the reader what O(Z) would be. Commented Jul 19, 2022 at 8:11
• Why not just use words? "The spaces \$O(X)\$ and \$O(Y)\$ have the functions \$g(x)-f(x)\$ and \$g(x)-f(x)\$ defined on them, respectively." Commented Jul 19, 2022 at 13:09
• Tangentially to the issue of the parentheses, the wording “has functions defined on it” is vague and nonstandard. It makes it hard to discern whether the sentence is a definition or a claim, and makes me wonder whether those are all the functions that the space has, or can there be other ones. Commented Jul 19, 2022 at 16:06

@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))...

• Agreed: It is better not to separate two formulas with mere punctuation. Commented Jul 19, 2022 at 2:38
• alternatively, or respectively, any of the two wordings will do. Commented Jul 19, 2022 at 8:28
• In my experience "respectively" is much more common; I first read "alternatively" here. Commented Jul 19, 2022 at 11:04
• Isn't ‘respectively’ usually abbreviated to ‘resp.’? (Maybe not for the first usage, but for subsequent usages.) Commented Jul 19, 2022 at 12:38
• As @gidds says, "symbols (resp., moresymbols)" is a common mathematical usage. The "resp." breaks up the symbols, and strongly suggests that the parentheses are not mathematical. Commented Jul 19, 2022 at 19:05

As Federico Poloni points out, it is customary in mathematics writing to use "respectively", abbreviated as "resp.".

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?

• By convention, x is usually a member of X, etc.. I think it should be g(x)–f(x) (resp. g(y)–f(y)). Commented Jul 20, 2022 at 12:36
• I agree with this usage, at least in math, but FYI not everyone does. A reviewer of one of my papers said it was wrong, and in a more general context see: english.stackexchange.com/q/212549/109750 Commented Jul 20, 2022 at 12:44
• @Kimball That's very surprising to me. In the Computer Science / Mathematics papers that I read (and write!), this is clearly the common usage. I understand why it may sound incorrect, but it is, by a long shot, the easier to parse unambiguously to me. Commented Jul 20, 2022 at 14:12
• Oh, God. A (resp. B). It's a very useful, and completely ungrammatical piece of writing. I hate it, but have learned that my red pen of refereeing outrage cannot hold back this particular tide. For similar losing battles, see also: 'that' and 'which'; 'none is'; 'Jones's'; putting 'and' at the end of lists separated by a semicolon. Commented Jul 20, 2022 at 21:45
• The spaces \$O(X)\$ and \$O(Y)\$ have functions defined on them as \$g(x)-f(x)\$ and \$g(y)-f(y)\$ respectively. Commented Jul 21, 2022 at 15:58

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.)

• In (pure) math, I would find this use of square brackets weird (and similarly for braces, etc). They're usually just used for citations in plain text, though in math expressions some people do use them as you describe, e.g., x*[(y+1)^2-1/y]. Commented Jul 20, 2022 at 0:16
• Relying on typesetting (e.g. math mode vs. text mode) or using square/curly brackets is only confusing to the reader. It may be unambiguous, but it is not clear at all. And many formulas already have more than enough parentheses, so please do not mix them with text formatting and make it even harder to read.
– allo
Commented Jul 20, 2022 at 15:28
• Also worth saying that there are mathematical contexts where the type of bracket matters (for example \$f(x)\$ and \$f[x]\$, or \$(a,b)\$ and \$\{a,b\}\$, can have very different meanings). Be wary of confusing a reader in that way. Commented Jul 21, 2022 at 12:03

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