Missing $ inserted. Ha\"{i}

Question

When I extend my code into a small example.
My tex code is:

\documentclass[a4paper,11pt]{article}
\usepackage{mathrsfs}
\usepackage{latexsym}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage[usenames]{color}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{dsfont}
\usepackage{indentfirst}

\newcommand\D{\tilde{\Delta}}
\newcommand\dr{\mathrm{d}}
\newcommand\Dr{\mathrm{D}}
\newcommand\pa{\partial}
\newcommand\aro{\alpha\rho}
\newcommand\hlf{\frac{1}{2}}
\newcommand\me{\mathrm{e}}
\newcommand\axi{\alpha\xi}
\newcommand\thf{h_{hf}}
\newcommand\Si{\Sigma}



\def\lan{\langle}
\def\ran{\rangle}
\def\p{\partial }
\def\eps{\varepsilon}
\def\th{\theta}
\def\i{\sqrt{-1}}
\def\phi{\varphi}
\def\lam{\lambda}
\def\ga{\gamma}
\def\L{\mathcal L}
\def\M{\mathcal M}
\def\N{\mathcal N}
\def\F{\mathcal F}
\def\C{\mathcal C}
\def\R{\Bbb R}
\def\Z{\Bbb Z}
\def\Om{\Omega}
\def\pom{\p  \Omega}
\def\bom{\overline\Omega}
\def\ol{\overline}
\def\noo{\noindent}
\def\I{\mathcal I}
\def\D{\nabla}
\def\bphi{\overline\phi}
\newcommand\nnb{\nonumber\\}
\newcommand\allv{v_{tt},t^mv_{ss},t^mv_{st},v_s,v_t}
\newcommand\allg{G_{tt},t^mG_{ss},t^mG_{st},G_s,G_t}
\newcommand\dc{\dot{C}^}
\newcommand\hra{\hookrightarrow}
\newcommand{\pnorm}[1]{\left\|#1\right\|_{L^p}}
\newcommand{\abs}[1]{\left|#1\right|}
\ExecuteOptions{dvips} \marginparwidth 0pt \oddsidemargin 0.5 truecm
\evensidemargin 0.5 truecm \marginparsep 0pt \topmargin -25pt
\textheight 22 truecm \textwidth 15.0 truecm
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\renewcommand\baselinestretch{1}
\newtheoremstyle{mythm}{1.5ex plus 1ex minus .2ex}{1.5ex plus 1ex
   minus .2ex}{\kai}{\parindent}{\song\bfseries}{}{1em}{}
\numberwithin{equation}{section}
\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{eg}{Example}
\newtheorem{proposition}{Proposition}[section]
\newtheorem{remark}{Remark} [section]
\newtheorem{corollary}{Corollary}[section]
\allowdisplaybreaks[4]


\begin{document}

In \cite{brezis1983positive}, Brezis and Nirenberg discussed 
\bibliographystyle{plain}
\bibliography{ref}

\end{document}  

My ref.bib code in the following:

@article{brezis1983positive,
  title={Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents},
  author={Brezis, Ha{\"{i}}m and Nirenberg, Louis},
  journal={Communications on pure and applied mathematics},
  volume={36},
  number={4},
  pages={437--477},
  year={1983},
  publisher={Wiley Subscription Services, Inc., A Wiley Company New York}
}

When I build and see the latex, I have the following errors:

• Missing $ inserted. Ha"{i}
• Improper \spacefactor. Ha"{i}
• Extra }, or forgotten $. Ha"{i}
• Please use \mathaccent for accents in math mode. Ha"{i}
• Missing { inserted. Ha"{i}
• You can't use `\spacefactor' in math mode. Ha"{i}
• Please use \mathaccent for accents in math mode. Ha"{i}m Br'{e}
• You can't use `\spacefactor' in math mode. Ha"{i}m Br'{e}.

How can I correct this?

Answer 1

This is the minimal working example:

\documentclass{article}
\def\i{\sqrt{-1}}

\begin{document}

In \cite{brezis1983positive}
\bibliographystyle{plain}
\bibliography{ref}

\end{document}

When compiled with pdflatex (but not xelatex) it produces the said error. This is because \"i is translated to \"\i internally (I'm simplifying a bit), which triggers your redefinition of \i. And since square roots are defined in math mode, TeX is confused.

It is highly discouraged to use \def unless you know what you are doing. Use \newcommand or \renewcommand instead. Also, it is highly recommended that you do not redefine commands such as \i or \d. Because it will cause problems (such as now!).

As a final note, before asking technical questions --- not restricted to TeX or LaTeX related ones --- you should try your best to minimize your problem. Think of it as a challenge to use the smallest amount of code to produce the phenomenon you want to show. This process actually helps you, because it has a fair chance to already reveal the problem! On the other hand, this also helps others to diagnose the problem. In addition, you should provide some basic info, and if you are not qualified enough to judge whether a piece of information is relevant, you can provide it. For instance, the fact that xelatex copes just fine with your code will prevent others from investigating your problem.