Fun with infinity

It's not that hard to understand, really. You have infinite natural numbers. In those infinite natural numbers, there are infinite even numbers, and infinite odd numbers.

He said there were just as many even numbers as there are natural numbers. If limit calculus has taught me anything, there's different degrees of so-called "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!

You sir, are crazy xD