[Tex/LaTex] equal spacing for ‘ordinary’ limit and one-sided limit

Question

The problem is that one-sided limits have subscripted symbols above $a$. I tried adding a blank subscript to the 'ordinary' limit, but that didn't seem to even out spacing.

\underline{Theorem:} $\lim \limits_{x \to a^{}} f(x)
\Longleftrightarrow \lim \limits_{x \to a^{-}} f(x)
= \lim \limits_{x \to a^{+}} f(x)$

Answer 1

Use \vphantom{+} to have the same height as the RHS.

\underline{Theorem:} $\lim\limits_{x \to a^{\vphantom{+}}} f(x)
\Longleftrightarrow \lim\limits_{x \to a^{-}} f(x)
= \lim\limits_{x \to a^{+}} f(x)$