The set of real numbers is a field. - This is correct because the subject is "set" - one set singular; therefore, use the "s" form of the verb.
The set of all 3x3 square matrices does not form a group. - The same thing goes for this sentence as the one above.
The set of all beautifull English words forms a nice book. - The same thing goes for this sentence as the first two. The subject is "set" - one set.
One may easily feel inclined to use a plural verb in such sentences, and indeed some native speakers of English do. This is because the verb immediately follows a plural noun. However, the plural noun in all three sentences here is part of a prepositional phrase that follows a singular subject.
In all of them "The set of (some plural)" seems to play the role of a single singular unit. Am I wrong about it? <<
You are correct, and this is why we use the "s" form of the verb for present simple, which indicates a singular subject, not plural.
"The set of unitary 3x3 matrices with det U = 1 form the group SU(3)."
I think it should read forms - singular. What do you think? <<
It's hard to tell here. They use an equal sign. It depends on how many forms the set makes.
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