4

The code

\begin{alignat*}{2}
d\bigl(x^{(j)}_j, x^{(i)}_i\bigr)
    & \le d\bigl(x^{(j)}_j, x^{(i)}_j\bigr) + d\bigl(x^{(i)}_j, x^{(i)}_i\bigr)\\
    & < d\bigl(x^{(j)}_j, x^{(j)}_k\bigr) + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr) + d\bigl(x^{(i)}_k, x^{(i)}_j\bigr) & \text{$k$ arbitrary}\\
    & \phantom{d\bigl(x^{(j)}_j, x^{(j)}_k\bigr) + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr)} {}+ 1/i & \text{let $j\ge i$}\\
    & < 1/j + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr) + 1/j +1/i & \text{let $k\ge j$}\\
    & \le 2/i + \hat d\bigl( \overline{x^{(j)}}, \overline{x^{(i)}} \bigr) + 1/i & \text{taking $k\to \infty$}\\
    & < 2/j + 2/i & \text{since $j\ge i$}
\end{alignat*}

produces:

enter image description here

What is the cause of this miscalculated width of the box that \phantom creates? And how to get + 1/i placed directly below the + that appears in the above line?

1 Answer 1

8

You forgot to put {}< at the beginning of the \phantom.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{2}
d\bigl(x^{(j)}_j, x^{(i)}_i\bigr)
  & \le d\bigl(x^{(j)}_j, x^{(i)}_j\bigr) + d\bigl(x^{(i)}_j, x^{(i)}_i\bigr)\\
  & < d\bigl(x^{(j)}_j, x^{(j)}_k\bigr)
    + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr)
    + d\bigl(x^{(i)}_k, x^{(i)}_j\bigr) & \text{$k$ arbitrary}\\
  & \phantom{{}< d\bigl(x^{(j)}_j, x^{(j)}_k\bigr)
               + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr)}
    + 1/i & \text{let $j\ge i$}\\
  & < 1/j + d\bigl(x^{(j)}_k, x^{(i)}_k\bigr) + 1/j +1/i & \text{let $k\ge j$}\\
  & \le 2/i + \hat d\bigl( \overline{x^{(j)}}, \overline{x^{(i)}} \bigr)
    + 1/i & \text{taking $k\to \infty$}\\
  & < 2/j + 2/i & \text{since $j\ge i$}
\end{alignat*}

\end{document}

enter image description here

A better version with no \big delimiter and a couple of thin spaces next to the overlined symbols:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{2}
d(x^{(j)}_j, x^{(i)}_i)
  & \le d(x^{(j)}_j, x^{(i)}_j) + d(x^{(i)}_j, x^{(i)}_i)\\
  & < d(x^{(j)}_j, x^{(j)}_k)
    + d(x^{(j)}_k, x^{(i)}_k)
    + d(x^{(i)}_k, x^{(i)}_j) & \text{$k$ arbitrary}\\
  & \phantom{{}< d(x^{(j)}_j, x^{(j)}_k)
               + d(x^{(j)}_k, x^{(i)}_k)}
    + 1/i & \text{let $j\ge i$}\\
  & < 1/j + d(x^{(j)}_k, x^{(i)}_k) + 1/j +1/i & \text{let $k\ge j$}\\
  & \le 2/i + \hat d(\, \overline{x^{(j)}}, \overline{x^{(i)}}\, )
    + 1/i & \text{taking $k\to \infty$}\\
  & < 2/j + 2/i & \text{since $j\ge i$}
\end{alignat*}

\end{document}

enter image description here

1
  • 1
    Really dig the suggestion to have thin spaces around the overlined things. Wish I could upvote it one more time just for this!
    – Atom
    Feb 24 at 15:37

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