Well, you’re in for it now. Unless you have some sort of magical “GO BACK” button to go backwards in life you’re going to help her bring back Dini whether you like it or now. Maybe in the process Sarah will realize how silly this is and stop…or maybe…she’s on to something. You could get published!
“OKAY!” Sarah said. “I’m so glad you’re going to help me out, when I told my mom she told me I should go back to therapy. I’m just glad you believe I can do it. The first step is creating a free group that we can start rotating…I was thinking we could choose between these where S(a) is the free group starting with a, S(b), S(c)…of course S(a^-1) is in the not a direction.
“I know what your symbology means don’t patronize me,” you answer.
You’re looking at her free group set up, apparently, she has a lot of Dini directions she would like to sample in, not just two (a/b). You are way past questioning whether or not to accept the Axiom of choice at this point, you’re in it now. What do you pick?
F2 = {e} U S(a) U S(a^-1) U S(b) U S(b^-1)
F2 = {e} U S(a) U S(a^-1) U S(b) U S(b^-1) U S(f) U S(f^-1) U S(j) U S(j^-1)