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Originally Posted by Shocker
Given that S = (1 + 2 + 4 + 8 + 16 + . . .), if you multiply both sides by two, you get
2S = (2+ 4 + 8 + 16 + 32 + . . .).
Then, add one to both sides:
2S + 1 = 1 + (2 + 4 + 8 + 16 + 32 + . . .)
= 1 + 2 + 4 + 8 + 16 + 32 + . . . = S.
Thus, 2S + 1 = S.
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At this point, we have an impossible inequality.
2∞ + 1 = ∞
Clearly that is not possible. However I fail to grasp the algebraic rule that was violated.