The algebraic structure "Wheel" is a algebraic structure similar to field where zero is always defined, including division by zero. Fields (which includes the algebra most plebs work with) don't allow division by the absorbing element i.e. 0. Often, misguided people try to fix this problem by letting field be defined over (Q union inf). In other words, they let infinity be a defined element that equals a/0 where a is a element. However, this approach modifies the algebraic structure such that certain contradictions can be derived (1=2 for example). Therefore, this new construction is not a valid algebra. However, if extend our structure to include two new elements (two different types of infinity) and modify the structures distributive property, then we have defined what is known as a wheel. This structure is well-defined, behaves like a wheel in all the "normal cases", and allows for some cool behavior when we need to divide by zero. Interestingly, this structure is isomorphic to a 2D Riemann Sphere and resembles the complex numbers where the imaginary part is equal to 0.
Here are some links regarding the subject:
https://en.wikipedia.org/wiki/Wheel_theory
https://www2.math.su.se/reports/2001/11/2001-11.pdf
still more consistent than the reals.
Division by zero is valid is the order of the 0's and infinites is defined
e.g.
[math]0 * 1 = 0_1[/math]
[math]0 * 2 = 0_2[/math]
[math]frac{0_2}{0_1} = 2[/math]
[math]frac{1}{0_1} = infty_1[/math]
>[math] x/(x/x)/x = x^2[/math]
This never works for me.
But will it now?!
[math] 1 [/math]
it is frustrating
You can do better.
Instead of 0_1, 0_2, etc., just use 1*0^1, 2*0^1, etc.
Things work much nicer when you add a grading to the zero.
0^n is zero of degree n.
n being negative gives the infinities.
Structuring things in this way is obviously better. You essentially just get Laurent series.
but then 0*x=0 isn't true for all x
kind of makes 0 useless
It doesn't need to be. That's a stupid rule that exists for no reason, other than to approximate wheel algebras within the reals.
Create stupid rules, get stupid results.
yeah this isn't anything to do with 0 when you redefine it to be a boolean operator
in that same logic computers are constantly dividing by zero kek
I came to the same conclusion using algebra
>muh gay algebra
hitomi analysis won, get over it
Division by zero is undefined
> OP: Here is a definition of division by zero
> you: There isn't a definition of division by zero.
its not zero its some other made up bullshit
no it actually is zero, read the paper
you can make a wheel out of the natural numbers
that's like saying zero in complex numbers is some made up nullshit
Btw if you study classical optics you already know this
0*x=0 isn't true generally
kind of makes 0 useless doesn't it?
Now show us how division by zero would be useful in any context. Protip: you can't.
baseball season just started. a pitcher comes in and allows a run without getting an out. his earned run average (runs allowed per 27 outs) is a) infinite, or b) undefined?
the entirety of calculus is basically a cope about whether infinities exist or not
division is a searching algorithm
there is nothing to search for when dividing by zero
because there is nothing to search for, the algorithm cannot run
because the algorithm cannot run, it cannot produce a numerical result
because it cannot produce a numerical result in all cases, division is not an expression
if you make it return some non-numerical result in this special case, you introduce a new type of data, which is effectively what you are doing
unfortunately, this type of data is useless, and has no semblance of similarity to the rest of mathematical expressions
>if we frick with the reals so that they are no longer reals, now we can divide by zero
wow great discovery
The political compass permanently damaged every single mind that even thought about accepting it just like this fricking wheel shit will do to you
One does not simply divide by zero!