/sci/ - Science & Math

>I am almost certain 0/0 is 0, because of this image.
In which wheel?

Is that another name for a ring?

Dare to resist, don't bump shit threads!

(except this post explaining to dare to resist to bump shit threads)

I don't want bumps i want answers

>>11462039
>by definition
>inverses
no the problem is that you people don't know a single thing about abstract algebra. People long before you have long since made sense of how and why division is possible, under what circumstances, etc etc.. I don't really have much else to tell except to read more ring theory

>>11462049
>Is that another name for a ring?
No.
https://en.wikipedia.org/wiki/Wheel_theory

I may be a dumbass, but aren't rings just sets with thingies you can do on them?

On the members of the set that is

>>11462067
Yes but they admit a lot more complicated behavior just by having simple structure on them.

Welp i believe you went above my vocab level. I am looking for a proof by contradiction, because i am too stupid to understand anything else.

>>11462078
Suppose we have a nonzero division ring or field. Suppose 0/0 is well defined and it equals 0. In general, when we have x = 0/0 (provided you accept basic facts about fields and rings), we say x is any number such that [math] x \cdot 0 = 0 [/math]. However, we see every such x satisfies this relationship, and so we get that every element is zero. However, we supposed that the ring was nonzero to begin with. Contradiction.

>>11462092
That is exactly my point, that since x is any number such that x * 0 = 0, therefore (0/0)*0=0

https://www.youtube.com/watch?v=uxpowBoPieQ

Why did we suppose the ring was nonzero?

>>11462095
Not really. This shows that 0/0 isn't a well defined number since it would have to be equal to everything in the ring.
>>11462099
There are some technical reasons, but it basically comes down to the core reason that [math] 1 \neq 0 [/math] in meaningful contexts. These two elements are considered distinct since if they are not, everything generally ends up being nothing but 0. That is to say, you could give 0/0 some form, but it's sort of a garbled mess that doesn't admit anything worth study.
So we keep 1 and 0, which are the multiplicative and additive identities, separate from our considerations.

>>11462097
anon isn't going to understand any nuances of quotient and mapping properties if he can't see why 0/0 isn't well defined in such a context

>>11462107
Why wouldn't they be considered distinct? I don't understand what you mean/

>>11462121
We supposed the ring is nonzero because then we have an element, at least a single element, that is nonzero. This means we have to consider a 0, which is our additive identity, and a 1, which is our multiplicative identity, and of course all sums of these elements, all multiples of the sums, all sums of the multiples, etc etc. So by supposing we have a nonzero ring, we encounter the first nontrivial case when examining a set of numbers. Namely, the integers are probably the most natural commutative ring to first thing about.

I still don't see what the problem with multiplying an indeterminate value that could equal any number in the set by 0 to make it so that it can only be 0 causes a problem

>>11462048
>In which wheel?
>>11462039
Wheel Theory
https://en.wikipedia.org/wiki/Wheel_theory
Anton Setzer - Wheels
http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf
Jesper Carlstrom - Wheels: On Division by Zero
http://www2.math.su.se/reports/2001/11/2001-11.pdf

wheels bro, keep on rollin'

>>11462134
because 0/0 is clearly not well defined. If we follow the contradictory argument, it is every arbitrary element in the field. What this means is one of two things
1) 0/0, which we assumed is an element, is actually a set of unique elements that aren't zero. Contradiction (a type theoretic argument would probably be better here)
2) every element in the ring satisfies x * 0 = 0 by definition of 0, so every element in the ring is 0, but we assumed otherwise. Contradiction

Both of these are consequences of the fact 0/0 isn't well defined.

>>11462149

its not just division, it is also multiplication by 0

>>11462048
>>11462141
There are wheels within wheels in this village, and fires within fires!

>>11462162
No, this is specifically division by zero. Multiplication by zero is well defined.

who will save /sci/ from this daunting unanswered question?

>>11462039
0/0 generates a completely new set of reals. Any system by which 0/0 is allowed is, by necessity, 2 dimensional.

>>11462039
Lmao. OP is retarded. What did you prove from the image. Nothing. You in essence just multiplied both sides by zero. The result nothing.

Let's start with your argument
0*0=0
Now divide both sides by zero
0*0/0=0/0
0*(0/0)=(0/0)
Well..... we're back to square on. The LHS and RHS are not defined. Hence your argument is false. Try again next time.

>>11462256
No one. Because the argument is fallacious.

>>11462141
Wheel theory doesn't solve shit, that stupid cross thing is just as much of a dead end as 0 and infinity

>>11462039
division is the inverse of multiplication, and there is no unique inverse for zero because x * 0 = 0 for all x. at worst you can argue that it's multivalued, at best you can define something like a projective coordinate system and introduce a point at infinity

>>11462039
OP, if you're a brainlet (which at this point I think you're) and still can't comprehend the veracity of your claims, there's an easier way to understand.

Consider the ratio 1/x
What happens if we decrease x?
It becomes very large
Ex 1/0.1=10, 1/0.01 = 100, 1/0.0001 = 10000 and so on

now consider the ratio x/1 or just x.
What happens if we decrease x? It gets closer to 0.
Now multiplying both ratios seem to give us some intermediate answer.
Hence there's no specific number that can satisfy 0/0.

>>11462039
I'm starting to think that for f(x)=[0/0]*n, 0/0=1, while for f(x)=[0/0]+n, 0/0=0
Does that even make sense? A number that's 0 under addition, and 1 under multiplication?

>>11462039
0*1/0 = 0, 1=0

>>11463445
>Wheel theory doesn't solve shit
>that stupid cross thing is just as much of a dead end as 0 and infinity
Well, it sounds like someone knows less about wheel theory than wheel theory knows about him! Here's a little tip, kid: you can never hope to defeat your enemies without knowing how they think. And by the time you know enough wheel theory to fight the wheel theoretic, it's already too late. You're already a wheel theorist!

>>11462039
>"what times the denominator is the numerator", its the inverse of multiplication. Because of this, no matter what number you say 0/0 is its always multiplied by 0 and thus becomes 0.
But 0 times 1 is also 0, and 0 times 2, 3, 4, etc

Based retard OP trying to redefine basic math

>>11464081
>Based retard OP trying to redefine basic math
based retard defies the notion of algebraic structure

>>11463855
not an argument chap