Notation for setting a variable to an equality? Is there notation for setting a variable equal to the point where some expressions are equal? E.x. $$ c = (\sqrt{x}=2) $$ which becomes $$ c=4 $$ Because $$ \sqrt{4} = 2 $$
 A: There have been ideas like this before, for example Hilbert’s $\epsilon$ calculus, where you would write
$$
    c = (\epsilon x. \sqrt x = 2)
$$
(with the $\epsilon x$ indicating that you solve the equation for $x$), but none of these are common in current mathematics. Using words as recommended by TomKern in the comments is the usual approach.
You can also use
$$
    c \in \{ x | \sqrt x = 2 \}
$$
which also hints at the “problem” that solutions to equations need not be unique (or exist at all) and you need to specify what is supposed to happen in that case. (The $\epsilon$ operator simply returns some solution if one exists and a default element otherwise, so you need to check
$$\sqrt{\epsilon x. \sqrt x = 2}= 2$$ to make sure that $\epsilon x. \sqrt x = 2$ really is a solution.)
A: There may be some nuance here I am missing, but if you want to say that $c$ is a solution of $\sqrt x=2$,  I think what you want to write is just $$\sqrt c=2.$$
If this doesn't fully express your intended meaning, could you leave a comment saying how so?
