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I now see the subtle mistake in Shocker's 'cool math trick'.
Given S={1, 2, 4, 8 , 16...} and 2S={2, 4, 6, 8, 16, 32 ...},
then 2S + 1 = {1, 2, 4, 8, 16, 32 ...} IOW the infinite set called S and the infinite set called 2S has one less element than the infiinite set called 2S + 1. Yes they are all equal to infinity. But in each case, infinity has a different value. In the case of 2S + 1, the infinity also has one more element. Therefore we have equated infinities that are actually different.
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