You did not provide a test file that reproduces an infinite loop. If I complete your fragment to a document then LaTeX does not loop and the error highlights the typo in the environment name. If you are getting a loop that will be due to an unrelated error elsewhere in your file.
From
\documentclass{article}\usepackage{amsfonts}\begin{document}\begin {enumerate} % WEAK\item $G$ is a function such that for all $x \in \mathbb{R}$, $G(x) = x$\item $F$ is a function such that for all $x \in \mathbb{R}$, $F(x) = x$\item $x = y = 1$\end {eumerate}\end{document}
LaTeX reports:
! LaTeX Error: \begin{enumerate} on input line 5 ended by \end{eumerate}.See the LaTeX manual or LaTeX Companion for explanation.Type H <return> for immediate help. ... l.9 \end {eumerate}?
Of course the error from LaTeX is independent of the editor that you use to write the input file, so I wrote this test file in emacs but you would get the same if you had written it in TeXWorks.