Is $\mp a$ actually different than $\pm a$? So, the way I understand $\pm a$ as a general concept is basically as follows: $\pm a$ is really just two numbers, functions, or whatever $a$ represents, but the catch is that one of the $a$'s is positive, and the other is negative.
All of that makes sense to me. Mathematicians like to be efficient, but also precise, so they created a way to represent two (or more) entirely different objects, simply by using a special symbol.
These, then, are my questions:


*

*Is $\pm a$ actually different than $\mp a$?

*Why aren't there more these, if you will, Frankenstein symbols?

*If the answer to my previous question is, "There are," then why aren't they as common?


Standing by themselves $\pm a$ and $\mp a$ mean the same thing; usually the set $\{ a, -a \}$, such as solutions to some equation.
The notation $\mp a$ is a handy abbreviation in certain contexts. For instance
$$b_\pm = c \mp d$$
means $b_+ = c -d$ and $b_- = c + d$.
