# I've given up, missing $error. Help?  A subset$C$is \emph{closed} \iff \emph{$i\in C, i\to j$\implies$j$\in$C$} \\  Overleaf shows this where the error is. I've used my brain to find the error but no progress. Error is - missing$ inserted.

• The error indicates that some math maerial is not in math mode. \implies seems not to be, but i didn't test. How are you using the dollar signs right now? They seem to be more or less random. – Johannes_B May 14 at 5:32
• It is probably the \in . Try $j \in C$. – marmot May 14 at 5:38
• This compiles: \documentclass{article} \usepackage{amsmath} \begin{document} A subset $C$ is \emph{closed} $\iff$ $i\in C, i\to j \implies j \in C$ \end{document}. – marmot May 14 at 6:02
• If the answer provided below has solved the issues you were facing, please consider upvoting and/or "accepting" it. – Mico May 14 at 20:10

The directives \iff, \implies, and \in must all be executed in math mode. Separately, the \emph directive does nothing here, since it's a text-mode command whereas its argument consists entirely of math-mode material.

Hence, you need to replace

A subset $C$ is \emph{closed} \iff \emph{ $i\in C, i\to j$ \implies $j$ \in $C$ }


with

A subset $C$ is \emph{closed} $\iff i\in C, i\to j \implies j \in C$.


Better still, write

A subset $C$ is \emph{closed} if and only if $i\in C, i\to j$ implies $j\in C$.


Of course, you may choose to write "iff" instead of "if and only if".

A full MWE:

\documentclass{article}
\usepackage{amsmath} % for "\implies" macro
\begin{document}
A subset $C$ is \emph{closed} $\iff i\in C, i\to j \implies j \in C$.

A subset $C$ is \emph{closed} iff $i\in C, i\to j$ implies $j\in C$.
\end{document}

• Mavellous! The example at the bottom is (a) more readable, (b) has fewer characters to type, (c) is shorter when typeset. What's not to like? – Henning Makholm May 14 at 11:03
• @HenningMakholm - Many thanks for your compliment! – Mico May 14 at 12:29
• +1 for more words and fewer symbols. – Ethan Bolker May 14 at 15:17