I saw this a little while ago and wanted to figure out how to prove that it's invalid.
$$1+2+4+8+...+\infty= -1$$
Proof is as follows:
Knowing that $$1 * x=x$$ and that $$2-1=1$$ we can say that $$(2-1)(1+2+4+8+...+\infty)= -1$$expanding the brackets you get$$2+4+8+16+...+\infty- 1 - 2-4-8-...-\infty= -1$$ everything from 2 up cancels leaving $$-1=-1$$

Question

phoenixfire · Answer

However, if you do it for anything up to but NOT including infinity it is wrong.
$$(2-1)(1+2+4)=2+4+8-1-2-4=8-1=7$$Clearly not -1.

phoenixfire · Answer

Something to do with Divergent Series. but I don't understand it. 
$$\sum_{n=0}^{\infty}2^n$$

So I'm basically looking for a way to disprove the above claim for infinity.

unklerhaukus · Answer

$$\infty-\infty\neq0$$

phoenixfire · Answer

What do you get in the case of $$\infty - \infty=?$$Is there some law or rule that you can refer me to that explains that it's not equal to zero?

unklerhaukus · Answer

http://www.vitutor.com/calculus/limits/indeterminate_forms.html

unklerhaukus · Answer

infinity is not a number so you cant always treat it like a number, some times you indeterminate forms

phoenixfire · Answer

Well that makes sense now. 
I've always treated infinity as something unique and not a number, but when it came to this my brain got fried. 
Thanks, @UnkleRhaukus