Very simple number line with points

Do you mean something like

\documentclass[border=2pt]{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            % center the x axis
            axis x line=middle,
            % we don't need a y axis line ...
            axis y line=none,
            % ... and thus there is no need for much `height' of the axis
            height=50pt,
            % but `height' also changes `width' which is restored here
            width=\axisdefaultwidth,
            xmin=-3,
            xmax=3,
        ]
            \addplot coordinates {
                (0.5,0) (0.7,0) (0.9,0)
            };
        \end{axis}
    \end{tikzpicture}
\end{document}

A pure tikz alternative:

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
  \begin{tikzpicture}
    \draw (-3,0) -- (3,0);
    \foreach \i in {-3,-2,...,3} % numbers on line
      \draw (\i,0.1) -- + (0,-0.2) node[below] {$\i$}; % tick and their labels
    \foreach \i in {0.5, 0.7, 0.9}% points on line
      \fill[red] (\i,0) circle (0.6 mm);
  \end{tikzpicture}
\end{document}

With a simple picture environment without TikZ:

\documentclass{article}
\usepackage{color}
\begin{document}

\setlength{\unitlength}{1cm}
\makeatletter
%\fboxsep=.1pt \fbox{% debug for bounding box
\begin{picture}(6.3,.55)(-3.21,-.45)
  \put(-3, 0){\line(1, 0){6}}
  \multiput(-3, -.1)(1, 0){7}{\line(0, 1){.2}}
  \@for\x:=-3,-2,-1,0,1,2,3\do{%
    \put(\x, -.2){\makebox(0, 0)[t]{$\x$}}%
  }%
  \color{red}%
  \@for\x:=.5,.7,.9\do{%
    \put(\x, 0){\circle*{.1}}%
  }%
\end{picture}%
% }% end of \fbox
\makeatother

\end{document}