...but realized that in doing so, I had proved the opposite. Bummer!
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Assume that there are an infinite number of planets in the universe (i.e. that the universe is infinite). We know that not all planets are inhabited, so that must mean that the total number of inhabited planets in the universe is finite. Therefor, in order to find the average population of the universe (or the average number of planets that are inhabited), we do some basic math, dividing the number of inhabited planets (finite) by the number of total planets (infinite). Dividing any finite number by infinity gives you zero. Therefore, the average number of inhabited planets in the universe (and by extension the population of the universe) is zero, meaning none of us exists.