I believe this is correct: x/x = 1 everywhere except 0, where it has a removable singularity. So you can extend x/x holomorphically to full C.
This is completely different from the phenomenon described in the article: arccosh discontinuity can’t be dealt the same way. In fact complex analysis prefers to deal with it my making functions path-dependent (multi-valued).
This is completely different from the phenomenon described in the article: arccosh discontinuity can’t be dealt the same way. In fact complex analysis prefers to deal with it my making functions path-dependent (multi-valued).