People seem to be pretty critical of this post, but can anyone give me a good reason why math notation shouldn't have some concept of scope? I can't see any downsides. It would certainly help me puzzle out my professor's notes when he has used f to mean three different things in as many lines.
There is some concept of scope in math. At a fairly early level, a student learns sums and integrals. The variable of integration/summation's scope is just within the integral/sum.
At a higher level, some things have scope equal to a subfield of mathematics. A gothic p, for example, represents a prime ideal in algebraic number theory. It represents a parabolic Lie algebra in Lie theory. (Actually this causes problems when you're doing Lie theory and number theory at the same time.)
