Essay:What is 1 divided by 0

What is 1 divided by 0? That is a question that many have asked over the centuries. Most respond by claiming that it is undefined, and cannot be answered. Some claim that it is infinity, though this would mean that infinity would be finite, which is impossible.

I propose the idea of a number that has the properties of every number that exists. This will be referred to as W.

W is what I propose to be the wildcard number. This number has the properties of every number possible in mathematics, including itself. Therefore, W = 1 and W = 2 at the same time. This also means that W + 1 = W is true, and that W + 1 = 2 is also true, etc. It is paradoxical in nature, yet I believe that this might be a possibility. This, however, means that 1 does not equal 2. What I believe to be the possible definition of W is as a number that could be defined as the definition of a number, but without an absolute value. This also means that an equation involving W cannot be a function, since it is every number at once. So, 2 "wildcard" values could be represented by W2, or (W,W).

My reasoning for this is that if 1/0 = infinity, then infinity would not be the number of numbers in existence, instead it would mean that infinity = 1 = 2. A number with the properties of every number, W, is the only way to solve this paradox. This means that 1/0 = W, so 1/0 = 1, and 1/0 = 2, but 1 does not equal 2. I know that this is an incredibly short essay, and that this is confusing in many ways, but it solves a dilemma of infinity being a literal paradox.

Simplified
So, if W is every number at once, then W2 is (W,W). So, W3 would be (W,W,W), and so on. A guide to my hypothesis is that:
 * 1) W + n = W
 * 2) W - n = W
 * 3) W = any/every number
 * 4) nW = W
 * 5) W/n = W
 * 6) W2 = (W,W)''
 * 7) sqrt(W) = W
 * 8) Wth root(W) = 1
 * 9) Wi = W

This is only a hypothesis though. Take it with a grain of salt