Edit: the title was misleading, i didn’t ask about a rational agent, but about what comes out of certain inputs in Bayes theorem, so now it’s been changed to reflect that.
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 understood everything correct, then 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!