I feel confused about the meaning of "$D_{\infty}$ acts on the real line as the group generated by (affine) reflections across two distinct points."
where $D_{\infty} = \mathbb{Z}/2 \mathbb{Z}\ast \mathbb{Z}/2 \mathbb{Z}$
1 What are the reflections across two distinct points (I am asking the definition, I don't understand what a reflection across two distinct points is)?
2 How to see the group generated by (affine) reflections across two distinct points is just $D_{\infty}$?