Your characterization of Vinge's singularity is incorrect. I have never read anything in which he brings up infinity, I.J. Good does though. Vinge's is actually more like your AI revolution except that it will be evident as a singularity only to those looking forward and not to those looking backwards. So instead of using agriculture/industrial divide as an analogy he posits a human/animal divide.
As his definition of singularity is pretty strongly tied to comprehension think of it like this - the singularity is the time point after which a 10 year old unmodified human child from 1000 AD can not grow up to understand his or her surroundings.
I could have sworn that that argument came from a short piece of non-fiction Vinge wrote which was my first exposure to the whole idea, but I might be mis-remembering because it was a long time ago. Or, given that this was a long time ago, he might have changed his viewpoint.
As his definition of singularity is pretty strongly tied to comprehension think of it like this - the singularity is the time point after which a 10 year old unmodified human child from 1000 AD can not grow up to understand his or her surroundings.