*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!

Thanks for the answer! i was somewhat amused to see that it ends up being a zero divided by zero.

Does the ratio between 1epsilon over 2epsilon being undefined means that it's arbitrarily close to half (since 1 over two is half, but that wouldn't be

exactlyit)? or means that we get the same problem i specified in the question, where it could be anything from (almost) 0 to (almost) 1 and we have no idea what exactly?The latter; it could be anything, and by saying the probabilities were 1.0 and 0.0, the original problem description left out the information that would determine it.