It stands to reason that infinity plus two equals infinity. But, it stands to logic that infinity plus two doesn't equal infinity. Remember, you musn't confuse reason with logic. Reasoning speaking, if you are facing north, your back is facing south. But logically speaking, if you are standing on the south pole, you front is north, and your back is north. So remember... never ever confuse reason with logic.


Once upon a time there was an evil elf. He had a bunch of henchmen evil elves as to be named flees, due to their constant pestering of dogs. Both of these facts are two things you must remember, regardless of what this story says, and the final thing to remember is that the next statement is true.

Statement 1 is false.

Have I made myself clear?

The flea jumped onto a dog. That dog was a very normal dog. This dog had two fleas. He was very proud.

Another dog walked by. He had two billion fleas. As the law of equilibrium states, eventually both dogs had a billion fleas. How sad.

A person walked by. This person had no fleas. Fleas don't like people. The law of equilibrium doesn't apply here.

An elf walks by. He zaps the fleas, dogs, and person. They are burnt to crisp. The law of equilibrium is now completely impertinent. Yup, a very normal day.


You still with me? Good. I just wanted to know. You see, I am not going to ramble on about something useless today. This essay has mathematical substance and is actually useful! So let us proceed.

But wait a second! What if you don't want to learn? What if you want to be entertained? Then skip the first three chapters, they'll only bamboozle you, and go and check out Chapter 4! Nuf said!


First of all, I have to check whether or not you think infinity plus two equals infinity. If you do not think infinity plus two equals infinity, then please press the back button on your browser and select another essay to read.


Since you are still reading this, it would be reasonable to assume that you think infinity plus two equals infinity. If not, still read on. I'm always desperate for reviews!

First let's look at the reason behind having infinity plus two equal infinity. Infinity is an infinite amount of stuff right? So if we add anything to infinity then we still get stuck with infinity because infinity already has everything. Lost? No? Then let's proceed.

That theory is all well and good, so we can ask another question. What is infinity minus two? Infinity you would think. Since infinity is infinitally big, a puny finite number like two would not make a dent in it. So, we can safely say that:

Infinity + 2 = Infinity

Infinity - 2 = Infinity


Okay. Here's the next part. Since we've said I (Infinity) + 2 = I, then obviously I and 2 can be added together. If you disagree, you've just disproved yourself and I don't have to explain the rest to you. Otherwise, that is taken as a given. So, what happens when we have this?

Infinity - Infinity

Reason first. If we were to visualize infinity as a big force pushing you up forever, then -I would be a big force pushing you down. As a result, the two big forces would cancel each other out and you would stay at infinity, because that was where you started in the first place. Right? Never thought about it this way eh?

Then we have logic. Logically speaking, if you can add a + b, then that means that the property of a - a can take place. What we're saying is that this property:

a - a = 0

Any number subtracted from itself is zero! So:

Infinity - Infinity = 0

And here is where the paradox forms.

First of all, let's look at reason. We're saying that I - I = I. Of course, this technically is impossible because the rule that governs ALL numbers, including real and imaginary numbers, says that a - a must equal zero! It has to! So, if we take it this way, the only way we can have this happen is if Infinity - Infinity is in a set other than THE numbers.

WAIT A SECOND! That means that Infinity is a totally different concept from a number like 33! If the rules for numbers don't apply for infinities, then they can't be in the same group! That means... Infinity - Infinity doesn't equal Infinity! Because if it does, you have just disproved yourself! And you can't subtract two from infinity since that's like trying to subtract a triangle (abstract) from an apple (real).

Next, it's logic. Logic says that Infinity is part of the set of numbers because it obeys it's rules. Logic says that Infinity - Infinity = 0, which makes since with a - a = 0. But! By saying this logic has created another loophole for itself. And the culprit comes in the most unlikely form: THE ASSOCIATIVE PROPERTY!!!

The associative property is:

a + (b + c) = (a + b) + c

Which totally makes since, even in imaginary numbers! Since i is the square root of -1, which seems totally impossible, we can still make it work with the associative property! Imaginary 1 plus the sum of Imaginary 2 and 3 can be reversed around just normal.

Infinity, however, cannot. Watch:

Infinity - Infinity = Zero

Infinity - Infinity + Two = Two

Does that make sense? It stands to logic, because:

Infinity - Infinity + Two ?= Two

(Infinity - Infinity) + Two ?= Two

(0) + Two ?= Two

Two = Two

But, when we screw things up a little, things get into weird stuff.

Infinity - (Infinity + Two) ?= Two

Infinity - Infinity ?= Two

Zero X= Two

Obviously Zero doesn't equal two. But how, when we simply rearranged the order, we got two? Obviously something is amiss here. What I have just shown you breaks all the conventions of mathematics and some more about reality. So, I have just proved to you that Infinity - Two does not equal Infinity. In fact, we shouldn't even concern ourselves with such a problem, because infinity is an abstract abstract, and two is abstract. If we bring it down a level, we get apples and thoughts, and we're trying to do operations with them! Simply outrageous.

Well, well, well, I see that you are utterly bamboozled, completly confounded, and understood perfectly. Well, if you click on that review button that is below us, and fire away, I might be able to help you with your predicament.

Until the time after next time, maybe a few years before, warped with a double helping of a meat shake: