\documentstyle[12pt]{report}
\begin{document}

\begin{picture}(200,400)(0,0)
\multiput(0,0)(0,10){21}{\line(1,0){400}}
\multiput(0,0)(10,0){41}{\line(0,1){200}}
\put(30,30){$f(r_1)$}
\end{picture}

\begin{picture}(200,400)(0,0)
% number lines
\put(0,57){$R'$}
\put(0,107){$R$}
\put(0,50){\line(1,0){300}}
\put(0,100){\line(1,0){300}}

% points on the line
\put(60,57){$f(r_1)$}
\put(50,50){\circle*{3}}
\put(60,107){$r_1$}
\put(50,100){\circle*{3}}
\put(110,57){$f(r_2)$}
\put(100,50){\circle*{3}}
\put(110,107){$r_2$}
\put(100,100){\circle*{3}}
\put(260,57){$f(r_1+r_2)=f(r_1)+f(r_2)$}
\put(250,50){\circle*{3}}
\put(260,107){$r_1+r_2$}
\put(250,100){\circle*{3}}

% lower addition arrows and box
\put(50,50){\line(0,-1){40}}
\put(50,10){\vector(1,0){110}}
\put(100,50){\line(0,-1){20}}
\put(100,30){\vector(1,0){60}}
\put(160,0){\framebox(40,40){$+$}}
\put(200,20){\line(1,0){50}}
\put(250,20){\vector(0,1){30}}

% upper addition arrows and box
\put(50,100){\line(0,1){40}}
\put(50,140){\vector(1,0){110}}
\put(100,100){\line(0,1){20}}
\put(100,120){\vector(1,0){60}}
\put(160,110){\framebox(40,40){$+$}}
\put(200,130){\line(1,0){50}}
\put(250,130){\vector(0,-1){30}}

% connecting map
\put(50,90){\vector(0,-1){30}}
\put(100,90){\vector(0,-1){30}}
\put(250,90){\vector(0,-1){30}}

\end{picture}

\end{document}


