I'm trying to write a piece of code in LaTeX which includes a crossed set of arrows (the \nearrow and \searrow). Here is my code
\documentclass{article}
\begindocument
$$\dfrac{5}{12}\makebox[0pt][l]{$\,\,\nearrow$}\searrow \dfrac{20}{9}.$$
\end{document}
The code is doing what I want it to do but I am noticing errors, namely
unclosed $$ found at $ unclosed open group { found at $ unexpected $ after open group { unexpected $ after $$ unexpected $ after $$
I can't seem to understand how to resolve this and get the symbol I'm looking for. After some research I learnt about a \toea command but I can't seem to implement this. Any help would be great!

\begindocumentwith\begin{document}, and please peruse and take to heart the posting Why is\[ ... \]preferable to$$ ... $$? – Mico Jul 18 '23 at 23:57! Undefined control sequence. <recently read> \begindocumentyou get! Undefined control sequence. l.3 $$\dfracthe message you do show is not from tex. – David Carlisle Jul 19 '23 at 00:00