How do I generate a less than symbol and vertical bar that are the same height?

Question

In a particular document I need to produce a less than symbol next to a vertical bar. The two symbols need to be the same height. I have used \textbar \textless but the less two symbols are not the same height. I don't mind which symbol is made larger or smaller, as long as they are the same height.

(I will also need to do the same with a greater than symbol, and a broken vertical bar).

Answer 1

Here is an answer of what I can imagine you mean:

\documentclass{article}
\usepackage{textcomp} % for "\textbrokenbar"
\begin{document}
$\langle\vert$ $\vert\rangle$ 
$\langle$\textbrokenbar\ \textbrokenbar$\rangle$ 
\end{document}

Output:

Answer 2

Maybe like this?

\documentclass{article}
\usepackage{textcomp} % \textless, \textgreater, \textbrokenbar macros
\usepackage{graphicx} % \resizebox macro

%% Premiliminaries
\newlength\myheight
\settoheight{\myheight}{\textless}
\newcommand\raisedtextbar{\raisebox{0.4ex}{\textbar}}
\newcommand\raisedbbar{\raisebox{0.4ex}{\textbrokenbar}}
\newcommand{\mybar}{\resizebox{!}{\myheight}{\raisedtextbar}}
\newcommand{\mybbar}{\resizebox{!}{\myheight}{\raisedbbar}}

%% Four user macros (adjust the kerning to taste):
\newcommand\ltbar{\textless\kern-0.5pt\mybar}
\newcommand\bargr{\mybar\kern-0.5pt\textgreater}
\newcommand\ltbbar{\textless\kern-0.2pt\mybbar}
\newcommand\bbargt{\mybbar\kern-0.2pt\textgreater}

\begin{document}
\ltbar{} \bargr

\ltbbar{} \bbargt
\end{document}

Answer 3

Just one guess, namely that the strokes are 7.5% of the height of the less than symbol.

\documentclass{article}
\usepackage{pict2e}

\makeatletter
\newcommand{\lgbar}{\mathrel{\mathpalette\dehaer@lgbar\relax}}
\newcommand{\dehaer@lgbar}[2]{%
  \vcenter{\hbox{%
    \sbox\z@{$\m@th#1<$}%
    \setlength{\unitlength}{\dimexpr\ht\z@+\dp\z@}%
    \linethickness{.075\unitlength}%
    \begin{picture}(.225,1)
    \roundcap
    \polyline(0.1125,0)(0.1125,1)
    \end{picture}%
  }}%
}
\newcommand{\lgbbar}{\mathrel{\mathpalette\dehaer@lgbbar\relax}}
\newcommand{\dehaer@lgbbar}[2]{%
  \vcenter{\hbox{%
    \sbox\z@{$\m@th#1<$}%
    \setlength{\unitlength}{\dimexpr\ht\z@+\dp\z@}%
    \linethickness{.075\unitlength}%
    \begin{picture}(.225,1)
    \roundcap
    \polyline(0.1125,0)(0.1125,0.4)
    \polyline(0.1125,0.6)(0.1125,1)
    \end{picture}%
  }}%
}
\makeatother

\newcommand{\ltb}{<\lgbar}
\newcommand{\gtb}{\lgbar>}
\newcommand{\ltbb}{<\lgbbar}
\newcommand{\gtbb}{\lgbbar>}

\begin{document}

$a\gtbb b\ltbb c \gtb d\ltb e_{\ltb}$

\Large
$a\ltb b$

\end{document}

Answer 4

\documentclass{article}
\usepackage{scalerel,textcomp}
\newcommand\ltbar{%
  \mathrel{\ThisStyle{\stretchleftright{.}{<\kern-10\LMpt\kern6pt}{$\textbar$}}}}
\newcommand\ltbbar{%
  \mathrel{\ThisStyle{\stretchleftright{.}{<\kern-9.5\LMpt\kern6pt}{$\textbrokenbar$}}}}
\begin{document}
$a\ltbar b_{x\ltbar y}\ltbbar c \ltbbar d_{x\ltbbar y}$
\end{document}