Underfull \hbox (badness 10000) in paragraph despite using tabular in wizard

Question

I've read the other topics on this but I really cannot understand why I'm getting it in my case when it has been made by the wizard rather than by hand. I have

\documentclass[a4paper,11pt]{article}
\usepackage{graphicx}
\usepackage{framed}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{array}
\usepackage{enumitem}
\usepackage{amsthm}
\newtheorem*{eg}{Example}

\begin{document}
\begin{itemize}
\item[\textbf{4.}]
\end{itemize}
Let $A=[0,1] \setminus \mathbb{Q}$.\\
\\
\begin{tabular}{|l||l|l|l|l|l|}
\hline 
space $X$ & $A^o$ & $\overline{A}$ & $\partial A$ & Is $A$ open? & Is $A$ closed? \\ 
\hline 
$\mathbb{R}$ & $\varnothing$ & $[0,1]$ & $[0,1]$ & No & No \\ 
\hline 
$\mathbb{R} \setminus \mathbb{Q}$ & $A$ & $A$ & $\varnothing$ & Yes & Yes \\ 
\hline 
\end{tabular} \\
\\
For $X = \mathbb{R}$, $\partial A = \overline{A} \cap \overline{\mathbb{R} \setminus A} = [0,1] \cap \mathbb{R} = [0,1]$.\\
For $X = \mathbb{R} \setminus \mathbb{Q}$, $\partial A = A \cap ((\mathbb{R} \setminus \mathbb{Q})_{<0} \cup (\mathbb{R} \setminus \mathbb{Q})_{>1}) = \varnothing$.

\begin{itemize}
\item[\textbf{5.}]
\end{itemize}
Proofs are in the notes.

\end{document}

Answer 1

The underfull hbox warnings are due to

\\
\\

as this forces two linebreaks with nothing in between so the resulting line is "under full" and infinitely bad (badness 10000 being as bad as TeX can report).

You should avoid all use of \\ outside its use to end table rows.

This has no warnings:

\documentclass[a4paper,11pt]{article}
\usepackage{graphicx}
\usepackage{framed}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{mathrsfs}
\usepackage{array}
\usepackage{enumitem}
\usepackage{amsthm}
\newtheorem*{eg}{Example}

\begin{document}

\setcounter{section}{3}
\section{}
Let $A=[0,1] \setminus \mathbb{Q}$.

\begin{tabular}{|l||l|l|l|l|l|}
\hline 
space $X$ & $A^o$ & $\overline{A}$ & $\partial A$ & Is $A$ open? & Is $A$ closed? \\ 
\hline 
$\mathbb{R}$ & $\varnothing$ & $[0,1]$ & $[0,1]$ & No & No \\ 
\hline 
$\mathbb{R} \setminus \mathbb{Q}$ & $A$ & $A$ & $\varnothing$ & Yes & Yes \\ 
\hline 
\end{tabular} 

For $X = \mathbb{R}$, $\partial A = \overline{A} \cap \overline{\mathbb{R} \setminus A} = [0,1] \cap \mathbb{R} = [0,1]$.\\
For $X = \mathbb{R} \setminus \mathbb{Q}$, $\partial A = A \cap ((\mathbb{R} \setminus \mathbb{Q})_{<0} \cup (\mathbb{R} \setminus \mathbb{Q})_{>1}) = \varnothing$.

\section{}
Proofs are in the notes.

\end{document}