You are assuming that infinity minus infinity exists, this is not a correct assumption. The problem is that your proof becomes invalid because one of the steps you used to prove is not correct.

Poop

Well this is confusing, but I am extremely intrigued and am going to do more in-depth reading on the subject. One thing: I notice people talking about realities in which we don't die and things like that. Well for this 'many-worlds theory' to work, (from what I've read and my own logic) the possibilities of each outcome happening have to be COMPLETELY equal. So, COMPLETELY 50:50 or whatever. The change that we will die is not 50:50. Out bodies simply wear out. And, for suicide which is mentioned here, of course the person wouldn't always live. There is not a 50:50 chance of them living or dying. (although sometimes there might be...) Just wondering, have you read "A Crack in the Line" by Michael Lawrence? (and its sequels) Not nessecarily recommending it, but just the fact that it refers to the many-worlds theory but not in the actual words... this makes me think of that book. I don't know if you get what I'm going on about here, is intriguing. I'm going to read more. The other two chappies were also interesting. I don't agree with everything here, but have gleaned some interesting and thought-provoking - I'm not by any means a physics professor or a researcher on quantum mechanics or anything! I'm just a 15-year-old girl who happens to be very smart and is top of her year. No bragging intended. My brain just works in an interesting way and likes to find logic in things, which is why I am going on about this. It's fun.

Great chapter _ I love this stuff. Keep it up. I always look forward to you updating this.
~Arayuldawen~

i like this.

wow, that one got my head spinning for a little while, heh. I just had to re-read some parts to understand. It makes sense, but at other times, doesn't make sense, well, in my head at least _ All of these chapters are just amazing. You are one intricate person.
~Arayuldawen~

Wow, that is just hilarious. The metric system is a whole lot easier, so it would make sense for America, a leading nation, to use an easier form of measurement. But alas, we never fully converted. Maybe someday in the future, that just might happen, heh.
~Arayuldawen~

wow, this one definitely made me think. The many-worlds theory, i hadn't heard of that, but it makes sense. I mean, I've thought of something similar to that, like if my parents didn't meet, then I wouldn't be alive...etc
Quantum Suicide, that makes sense also, because we'd always be taking the path where we go on, not where we die.
Great job on this chapter _
~Arayuldawen~

wow...That was incredible. That really made me think, with the 0th dimension and everything. How can you think of such interesting and confusing things? You are very talented _
~Arayuldawen~

{.99...1}. Yes, you have proved it. It means that the mathmatica value of .99... equal to 1. But it does not mean they are the same in all aspect. Obviously, they look very different. :)
This logic worked the same for your two sets of integers. Mathmatica equvalency can not help you here. Because they do not have mathmatic value, you can not compare them and say "a equal b". You can only compare them through other aspect. Obviously, The first set has the interger "1" and the other set does not. So they are different.
Take home message: think about what you are comparing.

For the experiment you described,please read the Wave-Partical Duality theory. Light is described as being
both waves and particles existing together in different domains, so is electrons and every partical in our life. You really don't need a Many-worlds theory to explain it.

"What makes infinity even more confusing is that it ties in with dimensions! Let's take the 1st dimension! That's a line. Wait... I'm getting ahead of myself. There should be a 0th dimension! (scratches head) The 0th dimension is a coordinate point, like a dot, except it has no substance, it is infinitsimally thin and infinitsimally short. That, my friends, is the 0th dimension. "
According to your definition, 0th dimension should be 1/infinity, not 0.
That will solver your later problem because (1/infinity) x infinity can be 1 (line). Like I said before, it's not meanful to use infinity to do math, because the result could be anything. Actually 0 x infinity could be 1.

For infinity 2 question: Infinity is a definition, not an actually number. You can not do math using it and expect a reasonable number. By definition, when you say "Infinity 2 Infinity", it already mean "Infinity - Infinity / 0" because otherwise "20".

All I have to say, is that this is pure brilliance. I'm not good with normal math, but stuff like this, I'm a genious, so this essay is perfect for me.
HHmm... My favorite part would have to be the Quantum Suicide one though, I'm quite partial to Quantum theory/physics/mechanics.
But still, excellent job!
(and yes, I did understand everything you said, amazingly enough)

I was about to send you a review smashing your ideas, but upon rereading it it does make sense. Sort of.