# Proper inter-column spacing and vertical alignment in a tabular environment

I have code for a tabular environment that is not displayed properly. I have the right parenthesis following the lower-case Roman numerals i, iii, and v aligned, and I would like to have the right parenthesis following the lower-case Roman numerals ii, iv, and vi aligned. I thought that I had made the inter-column spacing 1.5 inches ... but that didn't happen. Why didn't the command \hspace*{2em} preceding the tabular environment indent the left edge of the box containing the contents of the tabular environment by 2em? (I know there are other packages to use to display this table. I want to use the tabular environment and have my code modified.)

\documentclass{amsart}
\usepackage{amsmath}

\begin{document}

\noindent The following sets have either a least upper bound or a greatest lower bound of 1. \\
\noindent \hspace*{2em}
\setlength{\tabcolsep}{1.5in}
\begin{tabular}{r@{}lr@{}l}
\textbf{i.) }   &   $\displaystyle{\left\{1 - \frac{1}{n} \mid n \in \mathbb{N}\right\}}$
\textbf{ii.) }  &   $\displaystyle{\left\{1 + \frac{1}{n} \mid n \in \mathbb{N}\right\}}$ \\[1.2\normalbaselineskip]
\textbf{iii.) } &   $\displaystyle{\left\{9\sum_{n=1}^{N} \frac{1}{10^{n}} \mid N \in \mathbb{N}\right\}}$
\textbf{iv.) }  &   $\displaystyle{\left\{1 - \left(\frac{1}{2}\right)^{n} \mid n \in \mathbb{N}\right\}}$ \\[1.2\normalbaselineskip]
\textbf{v.) }   &   $\displaystyle{\left\{\sqrt[\uproot{1} \leftroot{-1} n]{2} \mid n \in \mathbb{N}\right\}}$
\textbf{vi.) }  &   $\displaystyle{\left\{\sqrt[\uproot{1} \leftroot{-1} n]{n} \mid n \in \mathbb{N}\right\}}$
\end{tabular}

\end{document}

• You are missing a & after the first math column, that's why the second roman number column is not aligned – user31729 Jan 4 '17 at 1:13
• You mention \hspace*{2em} but I don't see this instruction in your code. – Mico Jan 4 '17 at 10:52
• @Mico Thanks. I see that I have it highlighted on WinEdt; I must have gotten distracted before I hit Ctrl P and pasted it onto the code in my post. I just included it in the code. – A gal named Desire Jan 4 '17 at 12:24
• @AgalnamedDesire - Indeed, providing the previously-missing \hspace{2em instruciton makes a big difference. I will update my answer accordingly. – Mico Jan 4 '17 at 12:53
• @Christian Hupfer Thanks. I posted a response that included your suggested edit. Why is the tabular environment shifted rightward so much? – A gal named Desire Jan 4 '17 at 14:39

Something like this?

\documentclass{amsart}
\usepackage{array}
\newcolumntype{L}{>{$\displaystyle}l<$}
\newcommand\mmid{\;\middle\vert\;}
\begin{document}

\noindent
The following sets have either a least upper bound or a greatest lower bound of 1.

\setlength{\tabcolsep}{0.25in}
\setlength{\extrarowheight}{3ex}
\begin{tabular}{@{} *{2}{r@{\hspace{1em}}L} @{}}
\textbf{i.)}   &
\left\{1 - \frac{1}{n} \mmid n \in \mathbb{N}\right\} &
\textbf{ii.)}  &
\left\{1 + \frac{1}{n} \mmid n \in \mathbb{N}\right\} \\
\textbf{iii.)} &
\biggl\{9\sum_{n=1}^{N} \frac{1}{10^{n}} \biggm|N \in \mathbb{N\biggr\} &
\left\{1 - \left(\frac{1}{2}\right)^{n} \mmid n \in \mathbb{N}\right\} \\
\textbf{v.)}   &
\left\{\sqrt[\uproot{1} \leftroot{-1} n]{2} \mmid n \in \mathbb{N}\right\} &
\textbf{vi.)}  &
\left\{\sqrt[\uproot{1} \leftroot{-1} n]{n} \mmid n \in \mathbb{N}\right\}
\end{tabular}
\end{document}

• This display is very close to what I want. The lower-case roman numeral iii seems to be at the left margin. I think that putting the \noindent \hspace*{2em} before the tabular environment will shift it rightward appropriately. (I forgot to put that in my original post.) – A gal named Desire Jan 4 '17 at 12:40
• What do the @{} *{2} and the @{} instruct TeX to draw for the tabular environment? – A gal named Desire Jan 4 '17 at 12:40
• @AgalnamedDesire - I've updated the answer and screenshot to incorporate the piece of information about \hspace*{2em}. In a tabular setup *{2}{...} means that the material in the second curly brace is performed twice. @{} suppresses any whitespace in that location. – Mico Jan 4 '17 at 13:01
• @Mico, great answer. In my attempt, to solve that problem on my own, I added \newcolumntype{R}{>{\bfseries}r<{.)}} to the preamble. Hence I only wrote i & \left ... into my table body. Saves also some typing trouble. – Jan Jan 4 '17 at 14:03
• @Mico I posted a response to ask you the following question. Why is the display of the tabular environment in my code shifted a lot more rightward from my code more than the tabular environment from your code? – A gal named Desire Jan 4 '17 at 14:15

I think it is easier to use a dedicated tool for what you want to obtain, namely the tasks package. Each \task is referable. I added a \set command for the set-builder notation, inspired by code in the mathtools documentation:

\documentclass{amsart}
\usepackage{showframe} \renewcommand{\ShowFrameLinethickness}{0.3pt}
\usepackage{mathtools}
\usepackage{xparse} %

\DeclarePairedDelimiterX{\set}[1]\{\}{\setargs{#1}}
\NewDocumentCommand{\setargs}{>{\SplitArgument{1}{;}}m}
{\setargsaux#1}
\NewDocumentCommand{\setargsaux}{mm}
{\IfNoValueTF{#2}{#1}{\nonscript\,#1\nonscript\;\delimsize\vert\nonscript\:\allowbreak #2\nonscript\,}}

\begin{document}

\noindent The following sets have either a least upper bound or a greatest lower bound of 1.

\settasks{label-width=2em, label-align=right, item-indent=4em, counter-format =\bfseries tsk[r].), column-sep=1in, before-skip=1.5ex, after-skip=1.5ex }
\task $\set*{1 - \frac{1}{n} ; n ∈ \mathbb{N}}$; \task $\set*{1 + \frac{1}{n}; d n ∈ \mathbb{N}}$;
\task $\set*{9∑_{n=1}^{N} \frac{1}{10ⁿ} ; N ∈ \mathbb{N}}$;
\task $\set*{1 - \left(\frac{1}{2}\right)ⁿ ; n ∈ \mathbb{N}}$;
\task $\set*{√[\uproot{1} \leftroot{-1} n]{2} ; n ∈ \mathbb{N}}$;
\task $\set*{√[\uproot{1} \leftroot{-1} n]{n} ; n ∈ \mathbb{N}}$.
`