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!

infinity minus infinity? That's either negative or positive infinity, so your calculation can't be done

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".

Infinity isn't countable, remember. With that being said, infinity/2 equals to infinity.