Then we do it all again for all the inverses $~$x^{-1}$~$, creating the functions $~$\\rho\_{x^{-1}}$~$\.
Pedantic remark: Aren't you missing the identity of free groups in your intuitive construction?
We have the $~$\rho_x$~$ and the $~$\rho_{x^{-1}}$~$. Where is $~$\rho_\epsilon$~$?
Comments
Patrick Stevens
Thanks: quite correct.