If that were so...

Agreed. Edit: I don't think the one claim means the other, but I do agree that the one (in this case) implies the other. Do you believe that the sky's being blue excludes its being (at the same time and in the same respect) red?

A student writing down "x>2" would have stated an infinity of beliefs about the answer.

Well, the student could be said to believe an infinity of things about the answer, not that the student has stated such an infinity. We agree that to state (or explicitly think about) an infinity of beliefs would be impossible.

Where is it located in your brain?

In response to Dave (the other one), I distinguished beliefs on my view into occurrent beliefs (those beliefs that do or have corresponded to some neural process) and extrapolated beliefs (those beliefs, barring any new information, my brain could predictably arrive at from occurrent beliefs). I am saying that I should be said to believe right now both all of my occurrent beliefs and all my extrapolated beliefs, and that my extrapolated beliefs are infinite. My extrapolated beliefs have no place in my brain, but they're safely in the bounds of logic+physics.

I plead the Chewbacca defense.

I...haven't heard that one.

There's another problem if you consider all the implications as if they were your beliefs, even if you've not explicitly followed the implication.

I don't think this, I agree that this would lead to absurd results.