[Question] Can a Bayesian agent be infinitely confused?

Edit: the ti­tle was mis­lead­ing, i didn’t ask about a ra­tio­nal agent, but about what comes out of cer­tain in­puts in Bayes theorem

Eliezer and oth­ers talked about how a Bayesian with a 100% prior can­not change their con­fi­dence level, what­ever ev­i­dence they en­counter. that’s be­cause it’s like hav­ing in­finite cer­tainty. I am not sure if they meant it liter­ary or not (is it re­ally math­e­mat­i­cally equal to in­finity?), but as­sumed they do.

I asked my­self, well, what if they get ev­i­dence that was some­how as­signed 100%, wouldn’t that be enough to get them to change their mind? In other words -

If P(H) = 100%

And P(E|H) = 0%

than what’s P(H|E) equals to?

I thought, well, if both are in­fini­ties, what hap­pens when you sub­tract in­fini­ties? the in­ter­net an­swered that it’s in­de­ter­mi­nate*, mean­ing (from what i un­der­stand), that it can be any­thing, and you have ab­solutely no way to know what ex­actly.

So i con­cluded that if i had un­der­stated ev­ery­thing cor­rect, than such a situ­a­tion would leave the Bayesian in­finitely con­fused. in a state that he has no idea where he is from 0% to a 100%, and no amount of ev­i­dence in any di­rec­tion can ground him any­where.

Am i right? or have i missed some­thing en­tirely?


*I also found out about Rie­mann’s re­ar­range­ment the­o­rem which, in a way, let’s you ar­range some in­finite se­ries in a way that equals what­ever you want. Dem, that’s cool!