Double line math sentence

Question

Hi, what's the best way to write this lines with that symbol between the rows

Answer 1

You didn't specify what TeX format is expected. I can show you how to do this in OpTeX:

\fontfam[lm]
\def\N{{\bbchar N}}
\def\rotin{\rotbox{90}{$\in$}}
$$
  \matrix{
      \N \times \N & \longrightarrow & \N     \cr
        \rotin     &                 & \rotin \cr
       (n,m)       & \longmapsto     & n + m  \cr    
  }
$$
\bye

Answer 2

I'd probably use an array, like this:

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}
\newcommand{\N}{\mathbb{N}}
\newcommand{\upin}{\rotatebox[origin=c]{95}{(\in)}}
\begin{document}
[
\begin{array}{@{}c@{~}c@{~}c@{}}
\N \times \N & \rightarrow & \N \
\upin & & \upin \
(n,m) & \mapsto & n+m \
\end{array}
]
\end{document}

I'm using \rotatebox from the graphicx package to rotate the symbols. I believe the stix package also defines an \upin command you could use directly.

The spacing with the upper right ℕ is not great, but I'm not sure there's a good way to solve that.

Answer 3

Here is a possibility with tikz-cd:

The ∈ symbols are labels on phantom arrows with the sloped option to follow the direction of the (invisible) arrow.

\documentclass{article}
\usepackage{tikz-cd, amsfonts}
\newcommand{\N}{\mathbb{N}}
\begin{document}
\begin{tikzcd}
\N\times\N\arrow[r] & \N\
(n,m)\arrow[r, mapsto]\arrow[u, phantom, "\in", sloped] & n+m\arrow[u, phantom, "\in", sloped]
\end{tikzcd}
\end{document}

Answer 4

Try this:

\documentclass[11pt,a4paper]{book}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[italian]{babel}
\begin{document}
\begin{alignat*}{4}
    \mathbb{N}\times\mathbb{N}  && \rightarrow && \mathbb{N}\\
    \rotatebox{90}{$\epsilon$} && && \rotatebox{90}{$\epsilon$}\\
    (n,m) && \rightarrow && n+m
\end{alignat*}


\end{document}

Output: