"The infinite dihedral groupD∞ is generated (as a subgroup of the group SR of

bijections : R ! R), by the translation t(x) = x + 1 and the reflection s(x) = −x of

the real line. Work out its elements, and find the orbit and the stabilizer of each of

the points 1, 1/2, 1/3"

I have to deal with that problem but i have no idea that how i am going to use that points. I once read that ts(x)= -x+1 has reflection in the point 1/2 but i dont know how.

Anyone to explain?