I've seen parenthetical comments that are inserted mid-sentence (like this) and I've also seen parenthetical comments that are inserted after the terminal punctuation symbol of a sentence. (Like this.)
Are both valid uses, and are there any more ways to use them?
I would always add a comment mid-sentence, unless of course the context called for it at the end anyway.
If I were to add a comment at the end then my British English education compels me to include anything that pertains to a sentence before the full stop (period), not after which I believe is the US English norm?
If one were to add comments at the end of the sentence, how would multiple comments be handled?
The condition was diagnosed during triage by Miss Daniels (a nurse) after she discussed the symptoms with Dr Hanson (a visiting GP).
I don't know a specific rule for this, but my usage for it is that a parenthetical comment in the sentence itself (like this one) comments on a specific aspect of something in the sentence. A parenthetical comment following the complete sentence is a comment concerning the sentence in general. (I hope that this is clear.)
The example here has the first parenthetical phrase commenting on parenthetical comments in a sentence; the second one actually makes a comment about the whole paragraph. To put it another way, the scoping of the inline comment is "something immediately proceeding me in this sentence", while the out-of-line comment is scoped to "the content of preceeding sentence or sentences".
Parenthetical comments and footnotes are signs of a lazy writer. You should avoid such devices both saying and not saying. Instead, make your choice to say it or not say it.
Parenthetical comments are appropriate only when the style dictates the express need to both say and not say something, such as the year in an APA style citation.
Aside from citation styles, there are infrequently applications for parenthetical comments in mathematical writing when a short consequence might help the reader understand a theorem's hypotheses. I'll provide some borderline examples, apologies for the mathematics :
If an involution σ fixes only finitely many elements in G,
then G has a definable (abelian) normal subgroup inverted by σ
and of finite index in G.
I've placed abelian into parentheses here because the reader probably knows that any subgroup inverted by an involution is abelian, but probably I should simply say abelian without the parentheses because superfluous consequences are perfectly fine.
For any sufficiently large (odd) prime ...
I'd consider this wrong because any reader knows that 2 is the only even prime, but this is the correct flavor for the usage.
Let G be an (infinite) simply group of finite Morley rank
Let G be an (infinite) simply group of finite Morley rank of odd type
The first is definitely wrong because finite groups have finite Morley rank, meaning that infinite is not a conclusion but a necessary hypothesis. The second is correct because infinite is a consequence of odd type, but I'd omit infinite entirely when writing for specialists.
It is clear that if such a comment required too many words in parentheses, then a sentence like "Recall that ..." would be more appropriate.
