Fun with infinity

Oooh Ahhh, playing with infinity!!! FUN FUN...

Let S be an arithmetic sequence as follow:
S = 1 + 2 + 4 + 8 + ... + 2n + ... {to infinity}

As we can see, S is a positive sequence, therefore
S > 0

Multiply S by 2
2S = 2 + 4 + 8 +...+ 2n + ... {to infinity}

Subtract S by 1 (by bringing the first term to the left hand side)
S - 1 = 2 + 4 + 8 + ... + 2n + ... {to infinity}

Oooohhh Aaahhhh!!! What do you know,
S - 1 = 2S

Now, let subtract S from both sides
-1 = S

But wait ..... we have already confirmed that S > 0, therefore
-1 > 0

qed!