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The division-by-zero type error is that EV(preventing holocaust|universe is infinite) would be calculated as ∞-∞, which in the extended reals is undefined rather than zero. If it *was *zero, then you could prove 0 = ∞-∞ = (∞+1)-∞ = (∞-∞)+1 = 1.

Hey, this might not really help, but here's a rough idea. I can think about it more thoroughly, or we can discuss this at some time, if you want.

Maybe you shouldn't consider the situation as two possibilities of a finite universe or infinite universe. An infinite universe is the limit of finite universes. Perhaps then you should consider an infinite universe as a sequence of finite universes, whose limit is indeed infinite, and work with that.

So for example, you will compute the difference in value in each of the finite universes, and take the limit of that, and use this as the value for the infinite universe.

This is a standard method in math and in physics. For example, in math this is formalized in pro categories (such as profinite groups), and in physics this is a sort of renormalization/regularization.

Bostrom discusses this possibility, but dismisses it as making the mere locations of people morally significant, because rearranging the terms in a sum can change the limit.

First of all, I think it is a reasonable assumption that there are only finitely many people in the universe, in which case the order does not matter.

Also, of course the location of people matter. If you move all earth people at this moment to mars, we will all suffer and die. In the same way, say there 100 other galaxies in which there is another earth. Move all of these people here, and we will have an enormous over population.