I wanna know what you guys think. Is this viable?

If 1 * 0 = 0 then 0 / 0 = 1.
If 2 * 0 = 0 then 0 / 0 = 2.

But if 0 / 0 = 1 and 2, then 0 / 0 = x.

If 1 * 0 = 0 then 1 / 0 = 0.
If 2 * 0 = 0 then 2 / 0 = 0.

And if 1 and 2 / 0 = 0, then x / 0 = 0.

So if 0 / 0 = x and x / 0 = 0 then x / 0 = x.

x / 0 = x

The problem ultimately comes from the fact that anything divided by 0 is undefined, so '0 / 0 = 1' cannot hold true, and anything else you build from there will fail. It's certainly possible to define division by zero such that it results in either 0 or the numerator. However, doing so ends up making math inconsistent with observation, and ultimately the practical goal of math is to be a model of reality. These sorts of models can be fun to play with, though, and you can derive interesting things from them or even discover new things!

For what it's worth, in the computer world the floating-point numbers (IEEE 754) deal with this with a "number" designated as "NaN" for "Not a Number", and a number designated as "Infinity". They define "0/0" as "NaN", "x/0 where x > 0" as "Infinity", and "x/0 where x < 0" as "-Infinity".

Is that purely computational or is there any actual mathematical proof(s) for dividing by zero equaling ±∞?

You can demonstrate that x/0 approaches positive infinity from the right and negative infinity from the left. You can't actually "equal" infinity in this sense as it's not a number, so we're taking a bit of a shortcut in the float world by defining some things to represent infinity such that we can assign it. You can't do anything numerical with those values, though.

one of the problems is there is no variable to combine with zero
and as zero counts as a numerical value
and as already stated anything divided by zero is undefined
this is faulty now if you had a variable say x it could make sense
but as already stated zero is not a variable and can't in most equations be equal to more than one whole numerical value when divided by its self
therefore 0/0= undefined
as it is in the calculator it just says zero

Just so you guys know, I only did this because I was bored. I guess I should've posted this in the jokes feed but I didn't think it fit. Sometimes when I am bored I do stuff like this which ultimately leads to learning something which is always cool.

P.S. Sorry I didn't clarify that in the first post.

It's important to keep in mind that there is no single mathematics. The real numbers, the decimals you are familiar with and the operations on them, do not include ±∞, but the extended reals do (and there's more than one way to do it!). Usually we choose not to define /0 for them either, but we still can! Moving up to complex numbers, the Riemann sphere sensibly defines x/0 = ∞ and x/∞ = 0 whenever x ≠ 0, ∞, matching our intuition that (number) / (really big) = (really small) and (number) / (really small) = (really big). (Notice though that ±∞ are the same!)

It does this while still following all the usual axioms of arithmetic, which is really the key in all this: you can define whatever you want as long as you carry out the rules it must follow. The Riemann sphere admits addition, multiplication, and division of all complex numbers except the cases I stated above. It's amazingly useful for complex analysis, which you might think of as a souped-up calculus.

You can define 0/0 if you want too, but if you do, as wheel theorists do, you must follow the rules it implies, which I would say are a bit counterintuitive for usual computational applications. But that doesn't mean they aren't useful! Just not for, say, IEEE 754, the floating point standard.

So, in all, dividing by zero isn't some deathly operation bound to unravel mathematics, or a pursuit that Big Professor doesn't want you to know about. It just turns out that it's not that useful most of the time, or messes with your arithmetic intuition if you take it too far and/or without caution.

If x/0 = x, then, say we were to get rid of the fraction. That means, we multiply both sides by 0. That gets us x = 0x. But wait...if x = 0x, then, say x = 1. 1 cannot equal to 0 times 1, which is 0. This holds true for any and every number. Thus, x/0 = x is simply incorrect.