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?


$\pm a$ and $\mp a$ represent the same thing.
However consider expressions:
$x \pm y \pm z$
and:
$x \pm y \mp z$
First one stands for either $x+y+z$ or $x-y-z$ while the second stands for $x+y-z$ or $x-y+z$. That's why we have two symbols.
