I think the word single is not necessary because the article a or an has done the job.
So the phrase "a single object" should be simplified as "an object". What do you think?
You are definitely right. Indefinite articles can be used only before single countable objects, therefore your assumption is right. It would be:
It would never be:
Your assumption is right and would create an unambiguous statement.
Single is there to put the emphasis on the fact that you are requesting a single object, not more. Imagine the following:
Even though in the above conversation the mother grammatically tells her daughter to add one apple, the apple may easily by understood as "a fruit", not "an object", and then the daughter may not know how many apples is she supposed to add and ultimately, she may add more than one.
If the mother said, try adding a single apple, it would be understood as "not more than 1 apple".
"Single" is just added for emphasis I think.
If the speaker had said "one dollar", it wouldn't have been as "strong" as when there was "single".
It's true the "a" and the "an" specify that the subject is singular, but "single" is for emphasis.
There is a tag on EL&U called 'single word requests'. This is not the same as *'word-requests'; it is asking specifically for one-word terms rather than phrases. Mathematically the two are equivalent, but as a matter of language they are different (it may be simpler to regard it as a matter of emphasis).
There are some situations with important differences. It is more than just an issue of significance, but one of clarity. The indefinite articles don't always mean "exactly one", but could instead mean "at least one".
For example, if I ask the question:
You can answer "Yes" if there is one or more apples in the box. Now suppose instead I ask:
You can answer "Yes" if there is one apple in the box, but normally you'd answer "No, there's more than one" if there is more than one apple.
Rimmer's last example also points out the difference. If I say:
A reasonable listener could interpret that to be one, or more than one apple. Whereas:
Is making it explicit that only one apple should be put in the pie.
Now be careful about situations where single seems to be equivalent to the indefinite articles. This happens when there are none of the objects and somebody would like to stress that point. For example, in the rhetorical question:
This doesn't mean the person is desiring just one apple, but more that they are appalled that not even one apple is available.
Generally you would be correct (although note that single has several closely related definitions, such as "unmarried," making it difficult to give a hard and fast rule).
The word single is often used for emphasis to draw attention to the solitary quality of the subject:
That is usually the case, but don't treat it as a rule, because it's not.
Unless they are being paid to write, people can use words the way they want to, and don't have to follow your, or anyone else's, personal preferences.
If I had a single penny for every rule that someone had invented for the English language, I'd never have to work again.