An appositive is often useful as a “context clue” for determining or refining the meaning of the word(s) to which it refers.

Facts not in the discussion matters less than what is actually being discussed.

It’s a bit of an oxymoron (silent isn’t really deafening - it just seems that way) as both (or all) are equally correct.

Elvis (or some lesser know artist) may have had many hits (or just 1), but the author’s context is all that matters.

So with - Elvis Presley’s No. 1 hit “Heartbreak Hotel” was released in 1956.

“This hit” is all that’s important to the author and if other hits need be disclosed, that a different story… for another time!

Elvis Presley’s No. 1 hit “Heartbreak Hotel” was released in 1956.

I have advised that, in the example above, though “Heartbreak Hotel” is clearly an appositive, it should not be set off with commas. Why? Because Elvis had more than one No. 1 hit. I further submit that to write that “Elvis Presley’s No. 1 hit, “Heartbreak Hotel,” was released in 1956″ would be to imply that Elvis had only one No. 1 hit.

I have also advised that, in the sentence “My brother Paul is 35 years old,” the speaker has more than one brother.
I have also advised that, in the sentence “My brother, Paul, is 35 years old,” the speaker has only one brother.

So far, so good. Morson’s, Chicago, and Gregg are in agreement on these points.

However, Debi has asked this question:

But what about the case of something like Elvis’s hit record? Presumably, most people know that Elvis had several, but what if we’re speaking of a performer whose number of hits isn’t readily known? Or how about if someone is talking about a boss? It’s possible to have several bosses, or only one boss. Or a pet? How do I know whether you have one cat or a dozen? Is the rule basically that if it’s *possible* to have more than one, no comma is necessary, but if it’s generally not possible, the comma is necessary? I’m always a little confused by this one, so your help and guidance would be most appreciated!

My response to Debi was an unequivocal “I don’t know.” And I don’t. I really don’t know, but I sure as heck want to know.

This is going to bug me to no end until someone comes up with an authoritative citation that directly addressed Debi’s question above