Math follows this as well but math deals with specific numbers usually.
Actually neither of the above is true. My apologies, but being somewhat in love with mathematics I feel inclined to address the completely irrelevant (and informally "correct") claim that math conforms to the pattern described or that it deals with specific numbers. Take the real number line: given any interval, there exists more numbers that are never specifically dealt with than there exists any numbers which are.
More relevantly, you raise a very good and absolutely essential point: equivalence vs. equality. In logic, we take every ascription of a property to any group as unqualified s.t. if x=y than y=x (and the linguistic formulation of the former would be "if x is y than y is x"). Clearly, this isn't generally true, for reasons such as those you point out. Of course, in general there isn't any word that isn't polysemous and in general the basic unit of language consists of constructions, and to the extent that we can informally define words we do so according to usage, not by asserting that "all theists are atheists" in contradiction to logic and usage and defended by asserting that poor grammar can defend what no dictionary, logic, or linguistic theory does.
This changes when we use sets and are no longer dealing with specific numbers.
Not exactly. For instance:
For instance we can say that x is a real number, but not all real numbers are x.
You are absolutely correct but with one caveat: we wouldn't say that this example is true in mathematics because "x is
a real number" is equivalent to "x is an element of R" not "x=R", which would be required to validly go from "x is a real number" to "x is [or isn't] all real numbers".
I am sorry, I don't know how to write this mathematically anymore.
Good point. Because formally we have the problem that
"there exists an
x s.t.
x is an element of R" vs. "x is R". In logic, "is" denotes equality & equivalence. In mathematics we have to be more careful, and by "x is a real number" we mean "x is an element of R" not "x is R"