Dividing by Zero

Brainlet here. If division is, in its simplest form, the amount of one number that is in another (E.G: There are four twos in eight, therefore 8/2=4), then why isn't anything divided by zero infinite? You can take an indefinite number of zeroes from any number, as it lacks a value, no?

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You can add an infinite ammount of zeroes and it still will be zero.

>then why isn't anything divided by zero infinite?
It depends what wheel you're working in.

en.wikipedia.org/wiki/Wheel_theory

There was an Indian mathematician who solved this; you have the indefinite idea right, but you can't divide nothing into nothing. 0/0 is called the indefinite form

If you work with only non negative numbers that works, since the limit from the right of 1/x as x goes to 0 is infinity. The problem is that from the left it's -infinity. Inituatively using you argument, you need -infinity of -0s to make a ppositive number to satisfy the laws of multiplying negative numbers. Since 0=-0 we get that the answer is both infinity and - infinity, thus undefined. Unless ofcource you work in some system where you loop infinity back to -infinity, then divition by 0 is defined.

Because in the extended reals -0 = 0 so you can't tell if you get +∞ or -∞

In the complex plane, -∞=∞=i*∞ so you can divide.

A reductive way to describe division is that the resulting quotient of division is the 'root' of linear addition - in the same sense that the result of the root operation is the root of linear multiplication. Then we may describe division of some number n by zero (in this setting) as: does there exist a number Q such that the sum of a set of Q zeroes is equal to n? ; of course, for non-zero n, this number is not definable, because no degree of summation will result in a non-zero sum, and for the case where n = 0, we have infinite solutions, because we necessarily have a zero-sum set.

Zero is not a number.

Came here to post this. Shine on you crazy diamond.

It should be noted this creates complex infinity.

Btw do mathematicians adopt a rule of least complexity? It seems like everyone working with reals are unwilling to extend when division by zero comes up and I was just wondering if there's some unwritten rule of simplicity being used

dose zero over zero equals one

Enough of this meme already

>this meme
What do you mean?

Wheels are meme. They don't have any decent properties, it's just a numberphile-tier meme structure

Name five practical applications for wheel theory.

Look in general terms its not allowed to devide numbers with 0 ( sry for bad english. I mean something like 8/0.)
But you can say that the denominator(i hope its right) goes infinitisimal against 0. So the smaller the denominator is, the bigger is going to be the number at the end.
I hope it was the right answer to your question, because this is how my prof. Explained it :)

You know if (lim x->0) for 1/x ----- you can see that the nu.ber at the end goes to infinte. But in general i dont know :)

This really doesn't have anything to do with limits. The limit never "reaches" zero, just gets arbitrarily close to it.

Say, f(x) = 0 when x=/=0 and f(0) = 1. Now the limit when x -> 0 is 0, but f(0) = 1.

Look at it like this, if we define division as multiplication by the reciprocal (which if I'm not mistaken is how it's typically defined, not that your how much into what definition is wrong it's just not mathematically rigid) we see 0 has trouble because it has infinite forms, ergo reciprocals. While every number has exactly one, simplest form and reciprocal (itself divided by one and vice versa, where all other values equal are reducible to this number) zero could be divided by any number to yield 0, and each would be in it's simplest form. Where would you begin to go about dividing? Multiplying by 1/0 sounds like a safe bet, but what if you chose 2/0? Well it wouldn't be any less correct would it? 0/2 is very much 0, and irreducibly so.
Without even touching upon the absurd notion of dividing by 0 we can see the procedure to do so itself is absurd, and therefore we say the number is undefined namely because it cannot be defined by the nature of math currently.

>algebraic structures must be useful
Now, that's a high school tier brainlet.

Take a load of bread and decide it up zero times. You still have the load of bread.

because 0 isn't a number so your definition of division can't apply to it

Cutting bread 0 times would be dividing the bread by 1, not 0. Cutting it once is dividing it by 2, you're 1 behind in your attempt at division mapping.

It doesn't have to be useful, but if isn't useful then it's a meme. If you like screwing around with memes that's your decision, but don't call it not a meme.

They don't have to be useful, but neat and have decent properties. Wheels are just clusterfuck where pretty much nothing but division by zero works

I was thinking about this and if 0.000...1=0 then wouldn't that prove that any number divided by 0 is 0?

Elaborate?

Well since 0.0000...1, where the ... stands for an infinite number of 0s, is the same as 0, then dividing by zero should in theory make the answer inifinity, right?

youtube.com/watch?v=BRRolKTlF6Q