Actualización 2 a petición de OP

Question

Quiero dibujar una figura (al dorso) como se muestra a continuación: un eje numérico con algunos intervalos indicados por el número encerrado en un círculo:

Answer 1

Actualización 2 a petición de OP

Creé un nuevo estilo llamado from inftypara representar el intervalo desde -infinity. Para colocar texto debajo de las figuras, nombré el cuadro delimitador hacha y coloqué un nodo debajo.

from infty/.style args={#1of#2}{%<-- new style "from infty"
            to path={($(\tikztostart)!#1!90:(\tikztotarget)$).. controls ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
                .. (\tikztotarget) \tikztonodes}}

\documentclass[tikz,border=5mm]{standalone}
%\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25},
             to infty/.style args={#1of#2}{%<-- new style "to infty"
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. ($(\tikztotarget)!#1!90:(\tikztotarget)$) \tikztonodes}},
            from infty/.style args={#1of#2}{%<-- new style "from infty"
        to path={($(\tikztostart)!#1!90:(\tikztotarget)$).. controls ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget) \tikztonodes}},
             to infty/.default={7mm of 0.4},
             from infty/.default={7mm of 0.4}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]
\begin{scope}[local bounding box=axe]%<-- bounding box "axe"
\coordinate (z') at (-2,0);
\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (-2,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
%\pic at (z) {tick};
\draw (z')to["4"{draw,circle},from infty](c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},to infty](z);
\end{scope}
\node[below] at (axe.south){My axis};%<-- node to add caption
\end{tikzpicture}

\end{document}

Actualización a petición del OP

Creé un nuevo estilo llamado to inftypara representar el intervalo hasta el infinito. Para colocar texto debajo de las figuras, nombré el cuadro delimitador axey coloqué un nodo debajo de él.

El código está comentado con %<--.

\documentclass[tikz,border=5mm]{standalone}
%\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25},
             to infty/.style args={#1of#2}{%<-- new style "to infty"
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. ($(\tikztotarget)!#1!90:(\tikztotarget)$) \tikztonodes}},
             to infty/.default={7mm of 0.4}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]
\begin{scope}[local bounding box=axe]%<-- bounding box "axe"
\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (0,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
%\pic at (z) {tick};
\draw (c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},to infty](z);
\end{scope}
\node[below] at (axe.south){My axis};%<-- node to add caption
\end{tikzpicture}

\end{document}

Parámetros de curva

Estos dos estilos están configurados, por defecto, aparece en la figura anterior. Es posible modificar elalturade la curva y sucurvaturacon los siguientes parámetros. Por ejemplo my curve=12mm of .4significa que la curva tiene unaalturade 12 mmy que elpuntos de controlde la curva de Bézier se encuentran en 0.4y 1-0.4=0.6del camino.

\draw (c) to["2"{draw,circle},my curve=12mm of .4] (b) to ["3"{draw,circle},my curve=8mm of .2] (a) to ["1"{draw,circle},to infty=15mm of .6](z);

Primera respuesta

Reutilicé elmi curva 7código que escribí aquí. Le cambié el nombre my curve.

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25}} 

Definí uno picque te permite dibujar una marca y escribir texto debajo.

pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}

Resultado:

Código:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,calc,quotes}
\begin{document}

\tikzset{my curve/.style args={#1of#2}{
        to path={.. controls ($(\tikztostart)!#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            and ($(\tikztostart)!1-#2!(\tikztotarget)!#1!90:(\tikztotarget)$) 
            .. (\tikztotarget)\tikztonodes}},
             my curve/.default={7mm of 0.25}}  

\begin{tikzpicture} [pics/tick/.style={code={\draw ++(0,-.2)node[below]{#1}--++(0,.4);}}]

\coordinate (c) at (1,0);
\coordinate (b) at (4,0);
\coordinate (a) at (6,0);
\coordinate (z) at (9,0);
\draw[-{Stealth[]}] (0,0)--(10,0);
\pic at (c){tick=c};
\pic at (b){tick=b};
\pic at (a) {tick=a};
\pic at (z) {tick};
\draw (c) to["2"{draw,circle},my curve] (b) to ["3"{draw,circle},my curve] (a) to ["1"{draw,circle},my curve](z);
\end{tikzpicture}

\end{document}