About infinity and zero undefined equations on simple algebra.
Considering x is a positive real number. Why can't we say that x / 0 = ∞. Since the bigger the divisor is, the more x will be closer to 0.
Also, why ∞ * 0 is undefined, isn't it just infinite zeros, thus resulting in a total of 0.
We can say that those two equations are not undefined, right?
>>7994240
x/0 = ∞
x = ∞ * 0
x = 0
But x is any positive real number. So you're contradicting yourself.
>>7994240
https://www.youtube.com/watch?v=lHdlHTsXbZg
Khan has a video on this subject in his algebra series.
>>7994266
x/0 = x ∞
x = x ∞*0
x = 0
Problem not solved.
>>7994254
>x/0 = ∞
>x = ∞ * 0
Not so fast, you'd have x * 0/0 = ∞ * 0, and so x * ∞ = ∞ * 0 = 0. You'll have to argue a bit differently here, the way you do it it looks like 0/0=1. Unless I am mistaken.
>>7994275
Yes well you already told us that x/0 = ∞. So 0/0 must be ∞. so we get
x ∞ = 0
Now how does that work?
>>7994254
So, I was wrong. Is there any objective answer to this or it'll always ends up contradicting itself?
I just want to know what would be the x solution for the equation 7/0=x, for example.
>>7994290
No, if there was an "objective" answer then it wouldn't be indeterminate. It could be anything depending on your reasoning.
>>7994289
I am not OP, and not saying that what he proposed wouldn't lead to trouble, either.
If x * ∞ = 0, you might have to argue why x = 0 then, but just "cancelling" the zero seems like an invalid shortcut.
>>7994296
I just tried to solve it by logic, is there another way of thinking the solution of indeterminates by logic like I did in the OP? What did I think wrong?
>>7994304
We already said from the start that x is any positive real number. And I didn't cancel the zeros.
>>7994316
>And I didn't cancel the zeros.
>x/0 = ∞
>x = ∞ * 0
What happens here, then?
>We already said from the start that x is any positive real number.
Yes, and that is why you showed that one arrives at the contradiction "x=0," showing OP's proposal to be useless. You are the one who posted the first reply, yes?
>>7994323
That's not what the post you replied to said.
And yes I posted that OP's assumptions cause a contradiction. So what?
ITT: high schoolers
>>7994345
But that's the defining property of division.
>>7994633
If 0/0=1, then x/0=∞ can't hold for x=0.
Now I see that OP said x>0 though, so eh.
Even if you'd get something different for 0/0 then, it would give a contradiction as pointed out in the first reply.
>>7994621
Yep, seems like most posters in this thread are disregarding that infinity and zero are expressions of ideas rather than numeric in nature
>>7994621
>>7994663
OP here. I can confirm that and I actually expected that most people that would come here wouldn't get past algebra to try to explain this, because thats what happens on these threads.
I know it's said they're limits rather than values, but I just wanted to know why I'm wrong in the OP, isn't it logically correct?
>>7994273
>>7994254
Maybe this happens because adding or multiplying infinity doesn't make any difference on infinity's value.
Thus the property of infinity "∞*2 = ∞" is what makes the contradictions such as 2=0 when 2/0=∞ appear.
It's as if any positive real number x had the same value (x=0) since it doesn't really matter to infinity's value.
tl; dr: The weird properties of infinity (mainly the ∞*x=∞) made the contradictions happen because infinity and finite numbers dont mix well.
Sorry for inpuring math with logic, /sci/.
>>7994240
> Since the bigger the divisor is, the more x will be closer to 0.
that's called a limit senpai .
also you can 'say' anything in mathematics by making a new axiom or w\e its just that we dont find axioms that contradict known mathematics and are generally useless very interesting .
what the fuck is division by zero like that does that mean ?
>>7995723
Here's my allegory to division by zero.
Division by two is sharing a certain number of candy to two people (you and your friend, for example).
Division by one is sharing the candy with one person (you for example).
Division by zero would be sharing the candy with no one (not even yourself), so it's as if you expelled the candy out of our universe so no one would ever have it.
>>7994266
This Anon did it right.
>>7994240
>what are limits
The problem is recovering you x value.
What about the geometric argument?
So you have a square with area 1. You 'cut' it into one piece; its area has to be 1 and you've essentially made no cut.
Next you cut the square into two equal pieces, each of area 1/2.
Next into four pieces, area 1/4.
Now you want to cut up this square into infinitely many pieces. What does their area have to be? Zero. So you can either cut the square into infinitely many lines or infinitely many points, since their areas are both zero.
Now the interesting thing is you can cram in the same number of points or lines into any shape with nonzero area; an infinite number
This to me at least suggests that x/[math]\infty[/math] = 0 for finite nonzero x.
>>7996387
>This to me at least suggests that x/∞ = 0 for finite nonzero x.
Also this can be trivially rearranged that x/0 = [math]\infty[/math]
You probably have to forbid some operations to avoid dumb things like 1=2 though I guess.
>>7996387
>Now the interesting thing is you can cram in the same number of points or lines into any shape with nonzero area; an infinite number
This actually has an interesting consequence, namely that given a 2D shape with an infinite number of points, you can't deduce its area.
>>7996403
>given a 2D shape with an infinite number of points, you can't deduce its area.
This basically explains the whole:
{1/[math]\infty[/math] = 0
2/[math]\infty[/math] = 0
1/[math]\infty[/math] = 2/[math]\infty[/math]
1 = 2} thing. Basically [math]\infty[/math]*0 (a collection of infinite points) can form any number (shape).
A division problem gives you the factor that will multiply by the divisor to give you the dividend. Therefor x/0 is saying, what multiplies by 0 to give you x. 0 is not a quantity - it is the absence of quantity. 0*x is like saying, give me no groups of x. Therefor there is no answer to the problem x/0.
>>7996387
>>7996390
>>7996403
>>7996409
This is why people should be taught calculus in a more intuitive, old fashioned way. If you only teach them about limits ad Riemann sums they miss out on the simple visualisation of an integral as a continuous sum of infinitesimal quantities. This lets physicists fly through mathematical problems instead of getting held up by the fine details. Some people might say this leads to errors where rigorous mathematics doesn't, but that isn't always true - sometimes the physicists are correct and the mathematicians are wrong, such as when string theorists decided to try their hand at enumerative geometry.
>>7996439
A-are you saying this is an incorrect way of looking at this issue?
>>7996439
I think in 8th grade our teacher showed us how to find the slope at a point by using an infinitesimal length of the line which was pretty intuitive. I think we also went through the entire proof over several days and made sure everyone understood what was going on, answering questions, etc.
I would feel really bad if they are just teaching people the rules to solve differentials and limits without any understanding, is that really the case?
>>7996439
> infintessimals
Disgusting
>>7994240
1/0=u
u*0=1
Problem solved.
>>7997578
Well sure, but x*0 and x*[math]\infty[/math] also doesn't give a unique result so you wouldn't expect the division by those to give a unique result either.
>not one person corrected it to lim x->∞
