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wadavis comments on On immortality - Less Wrong Discussion
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This. This matters.
This is more that metaphor. A exponentially larger infinity divided by a small infinity will be infinity. A exponentially small infinity divided by a large infinity will be zero. A division of proportional infinities will be a real number.
So if the chances of a Boltzamann Brain becomes increasingly less likely as enthropy increases. and enthropy increases as time approaches infinity, you have a division of infinities which can equal infinity, a real number, or zero. You won't know which without actually crunching the numbers.
As an aside, arguments that use infinite time come up enough that I'm trying to find a brief graphic or write up that teaches ∞/(2*∞)=1/2 and the ∞/(∞^2)=0. Any pointers?