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/sci/ - Science & Math

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7337626 No.7337626 [Reply] [Original]

Why isn't a regular number divided by zero infinity?

I don't know calculus or very complex math. Explain it like I'm 14

>> No.7337629

Because it ruins everything.

>> No.7337630

Why isn't it minus infinity?
-0.0...1 is pretty much the same as 0.0...1

>> No.7337635

If 3*4=12 then 12/4=3 and 12/3=4.
But if 7/0=inf then inf*0=7
But if 3/0=inf then inf*0=3
etc..etc..
0=1=2=3=4=5=...

>> No.7337648

Because that's approaching it from the positive side

For increasing numbers of x, 1/(1/x) => 1*x => x becomes bigger and bigger.

But if you approach it from the negative side, -1/(1/x) => -x approaches -infinity.

This is why dividing by zero is undefined, it's every number from and including -infinity to +infinity.

>> No.7337659

>>7337648
Sorry, I'm retarded

1/x

graph to illustrate: http://www.wolframalpha.com/input/?i=plot+1%2Fx

Basically as you approach 0 from the positive side, you approach infinity and as you approach 0 from the negative side, you approach negative infinity.

>> No.7337665

>>7337659
And now a /sci/ approved edit:

<span class="math">y=\frac{1}{x}[/spoiler]

>> No.7337667

Why isn't 0/0=1?

>> No.7337670
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7337670

>>7337635
this, even the most retarded kid gets this

>> No.7337672

>>7337626
Because if that were the case 1/x would be continous, and the limit of x approaching zero would then have to be this value, so it is infinite, but observe that it is also negatively infinite, therefore -inf = inf, which is a contradiction meaning the assumption was incorrect and therefore 1/0 is not infinity

>> No.7337673

>>7337626
You can define an operation which is just like division except that when you divide by zero it gives infinity, or even 37 if you want. It's just a less interesting operation than regular division, so nobody bothers studying it. There's nothing deep about division by zero not being defined

>> No.7337674

>>7337672
>Because if that were the case 1/x would be continous

no

>> No.7337676

Wow thanks sci.

>> No.7337680

>>7337626
Because division is defined as multiplication by the inverse number, and 0 has no inverse.

>> No.7337685

>>7337672
Why is -\infty=\infty a contradiction? Even calling it -\infty is a bit nonsensical since -a is just the additive inverse of a.
>>7337626
Well, dividing is multiplying by the multiplicative inverse, i.e. a number "b" such that for "c", c*b=1. But 0 can't really have a multiplicative inverse for obvious reasons. Maybe you could define 0*\infty=1 and have it be consistent, I dunno.

>> No.7337694

>>7337659
>>7337648
>>7337672
That's a retarded argument and not how it works.

If you take <span class="math">\mathbb{R}[/spoiler] with the indiscrete topology, <span class="math">(\emptyset,\mathbb{R})[/spoiler].
Then guess what? This is not a problem anymore, because everything converges to everything, but we still have that division by zero is undefined.

Why is that the case? Because the reason has nothing to do with analysis or topology.
It's purely algebraic, you cannot have a multiplicative inverse of 0 in any Ring except in the trivial ring. Period.

As stated by >>7337635, if you assume that's the case, you arrive at contradictions.

>> No.7337733

>>7337626
It tends to +infinity of -infinity depending on which side you approach zero from

1/1 = 1
1/0.1 = 10
1/0.0000001 = 10000000
etc

but

1/-1 = -1
1/-0.1 = -10
1/-0.0000001 = -10000000

>> No.7337750

>>7337667
Then this would be true:
0*3=0*4
Obviously true. By simplifying we have 0=0.
Divide both sides by 0
0/0 * 3 = 0/0 * 4
Was 0/0=1?
1*3=1*4
3=4
QED

>> No.7337830

>>7337680
>division is defined as multiplication
L0Lno

>> No.7337835

>>7337626
how many 2s fit into 8? 4. 2+2+2+2

how many zeros fit into 8? no matter how many times you add 0 to 0 it will always be 0, there is no answer

>> No.7337839

>>7337667
0/0 can be many things and it sort of depends on what situation you need to take 0/0 from:
http://mathworld.wolfram.com/LHospitalsRule.html

>> No.7337861

>>7337750
No.
If you set 0/0 = 1, that doesn't lead to any contradiction, you've just defined a new operation, that i'll denote //.
The thing is, // doesn't commute with multiplication like the old division used to.

0*3 = 0*4
(0*3) // 0 = (0*4) // 0
0 // 0 = 0 // 0
1 = 1

That's all you are allowed to do. You cannot re-order the operations to get (0 // 0) * 3 = (0 // 0) * 4, because you are using a new operation which doesn't behave like regular division does.

>> No.7337909

>>7337830
Yes. You only define addition and multiplication.

Division and subtraction are just notation.

>> No.7337924

>>7337909
He was probably thinking about divisibility. Bad luck, 0 is divisible by 0 but 0/0 is undefined

>> No.7337951

>>7337861
This is similar to calculating 2n/2 to become just n, or why not k2/k=2. k could be 0, for instance.

It is commutative that way. Division by n is defined as multiplication by n^-1, and mutiplication is commutative.

Basically (0*3)/0=0 * 3 * 0^-1=0 * 0^-1 * 3=0/0 * 3

>> No.7337977

>>7337951
> Division by n is defined as multiplication by n^-1,

Yes, of course.
But we're not talking about division anymore, we're talking about a new operation // which is "mostly like division but also 0 // 0 = 1"
This operation is not anymore the multiplication by the inverse.

There's really nothing deep about what i'm saying. All I'm saying is that you can define weird operations which behaves just like division except that they give arbitrary results when you "divide" by 0. Just like that guy was asking, "can't we just say that 0/0 = 1".
Nothing prevents you from defining such an operation, you're not going to get any contradiction from it. But this operation is not division anymore, so you lose pretty much all the usual rules, such as simplifying equations by dividing both sides.

>> No.7338100

>>7337694
It's a shame that this thread continued after this point, and that it will be back again tomorrow.

>> No.7338137

This is like the 4th divide by zero thread on sci right now kek:

A ring in which the additive identity has a multiplicative inverse is the trivial ring of 1 element.

The trivial ring of 1 element in not an interesting object of study.

You are free to work in a different algebraic structure that allows for division by zero. If you can construct one that can also recovers some kind of analogue to the basic properties of arithmetic that we would like to preserve, that would be most interesting.

Unfortunately, there is no such obvious algebraic structure that is as useful/interesting as the more standard objects such as rings and fields and algebras that we work with. If you discover it, let us know.

ps. when people ask about dividing by zero they are talking about dividing in the sense of division in a field or ring. Adding some retarded operation // doesn't add any interesting structure to the ring you're just playing games with notation and have added nothing new or interesting, you've just declared a relation 0//0=1. Who cares?

>> No.7338902

>>7337629
Lol, this is the simplest way it can be explained.

OP, watch this

5/0 = infinity
Therefore
5 = (infinity)(0)
5 = 0

You could do this with literally any number.

So basically it makes all of our shit fall apart.

>> No.7339023

>>7337635
Thus doesn't account fit different sized infinities