And, while pretty much everyone has denied the former, absolutely no one has disagreed with the latter. I freely state (not admit) here and now that the value of P(me|A) is one over a totally unimaginably large number. I fact, have loudly claimed this to be the fact numerous times. It is not infinity, but it is mind-bogglingly large. Large enough that the exponent is probably a mildly boggling number itself. I put an absolute bare minimum possible estimate on the value at 10 to the 80th power (1E80) factorial (i.e., 1E80 x (1E80 - 1) x (1E80 - 2) x (1E80 - 3) ... 4 x 3 x 2). That's a number so large that there may not be enough particles in the universe to write out the exponent in full, let alone the number itself. And I suspect it's bogglingly less than the actual value.
As I have said numerous times over the last year, if you can accept a finite number—any finite number, no matter how large—do so, and this debate can move forward!
Only in the sense that there'd now be two, which wouldn't share the mathematical property of identity. It could just as reasonably (or just as unreasonably) be said that the copy was you and the original no longer was. You're getting stuck in semantics. English is not designed to cope with the existence of two yous, but that's what we would essentially have. Two yous, both you in every reasonable sense, but still distinct and separate individuals.
Most importantly, the copy would have exactly the same sense of continuity and sense of self! Subjectively, both would be you! If you were teleported and copied at the same time, there would be no way of saying which had been teleported and which copied, subjectively or objectively, because teleportation is indistinguishable from destroying the original when creating a copy!
So yes, a perfect copy of your brain would produce the same you. There would now be two same yous, and we could tell them apart from each other, but neither would be THE same you. They would each be A same you. They would both be as much the same you as each other.
ETA: anyway, isn't all this arguing about whether it would be the "same you" just to try to get to infinity? When you just admitted that you don't need to get to infinity for your proof? Just forget about infinity and present your proof of immortality!