Math Philosophy-- Why does 1/∞ not equal 0, and for that matter, what is ∞?

Originally posted by PhysicsAdept
reply to post by UKLionheart

 

Would you say then, that .000000000000000000000000000000...1 equals 0?

Hahaha. No, because you can\'t have infinite 0 before the one. As soon as you put that one on the end, it is no longer 0., but with 0.999 going off into infinity, that's different!

Here's the proof of the0.99999 recurring thing:

Let's call x = 0.99999 recurring.

10 x= 9.999999 recurring

deduct x from both sides:

9 x = 9 therefore x = 1

therefore 1 = 0.9999 recurring.

Tralahhhhh!

reply to post by PhysicsAdept


Stop ignoring this

So let's assume 1/infinity = 0. That would mean 1 = infinity * 0.

But I'm sure you would also say 2/infinity = 0...which would mean 2 = infinity * 0.

Simple replacement gives you 1 = 2.

And explain how you resolve this paradox.

reply to post by PhysicsAdept

Would you say then, that .000000000000000000000000000000...1 equals 0?

It would never equal anything because it would be forever changing/growing.

x can be thought of as having infinite possibilities in our calculations, it can be scaled infinitely to from tiny to huge. It itself can never be infinite but it still represents infinity to a certain extent.

The Mandelbrot pattern can also be thought of as a representation of infinity.

Originally posted by UKLionheart
reply to post by PhysicsAdept

 

You said in your opening post that some infinites are larger than others. This is true. There are "countable" and "uncountable" infinities.

For example:

1 2 3 4 5....
1 4 9 16 25....

You can count the square numbers, but you cannot count decimals, because there is always another decimal place to add. you can however count fractions!!

Here is a really interesting documentary on infinity:
www.youtube.com...

Just a small correction.

I would say some infinite sets are larger than others.

Not that some infinities are larger than other infinities.

reply to post by OutKast Searcher


Well that is just the thing, it is no paradox... 1 will not equal 2. Frankly, I believe that you ignored me when I asked you nearly the same question. stop ignoring this:

Tsk tsk. Well alas I believe we are at an impasse. I greatly enjoyed everyone's ideas including yours. I cannot admit that I am wrong because I have yet to see how I am wrong. The problem with this question, "Why does 1/∞ not equal 0", or really it has involved into "What does 1/∞ equal", is that no one wants to deal with infinity. I tried to make my point, loud and clear, that we were assuming we could reach infinity.

Here is where the problem is.

Everyone (I generalize, nut not completely conclude it is EVERYone) with an education, as well as everyone without an education, does not seem to want to step out of the box for a second. The question is not what the limit is, nor what it means... well to an extent it is, but the real question and analysis is supposed to come after the point of infinity is reached. Now, my stance here is that, who knows if it is possible?

I know the definition of infinity, please do not insult me by saying I don't (or that I am missing fundamental skills, or that cannot grasp a limit). However, as a mathematician, I feel like it is (our) obligation to explore! It is (our) obligation to delve into the unknown and try to find out as much as we can!

Well, I get excited from it anyway. I mean, to just decide infinity as something that doesn't belong in an equation... it hurts a little bit. If infinity truly does represent everything, should we not attempt at the very least to incorporate it into an equation here and there? Mind you, it is not a number, but I stand by what I say! I wish to examine it as a number, as if it were one, as well as if it was this unstoppable force colliding into an unmovable object. Where is the harm in that? Infinity to me must act differently that the typical number though, because unlike the rationals, it is not constant. Unlike the irrationals it has no estimated definition. THAT is what I wanted to discuss. I want some speculation every now and again. Trust me, I am all about the numbers. I am the first guy to ask for the statistics of something and the math behind reasoning. But I have yet to see any undeniable proof of what you say, sorry.

Your proofs have been just as valid as mine in some ways, and also just as contradictory. Like on the other thread when you were talking about units... and how units are not generalizations, because they aren't exact they are based on society. Uh, yeahhh hello that would be a generalization.

Anyway, I wanted to explore what happened to that limit once x did in fact equal infinity. Remember, there is no proof to say it cannot happen, just speculation backing that it cannot. Because absence of proof is not proof of absence I chose to ascend into the chaotic realm of indeterminacy. I guess some people do not belong here--the textbooks cannot help them which must bring fear into their mind, clouding their vision.

With everything (I can currently think of) being said, I would like to point out that I do not believe you are wrong. Your entire purpose it seems is to prove that you are right. I will agree in front of all of ATS that I believe you to be correct, and this is why:



There is no such point to where you can not divide it further in math theory.

In reality, it depends on what you are talking about...and in reality things are finite, not infinite.



True, in the real world that is true. We live in the real world, and thus it is true. However, I think this quote helps my case more than yours, outside of the real world. In reality, things are finite, not infinite. I wasn't walking about reality, I was talking about sub-reality. Ya know, where the plane of infinity exists. The imaginative side of math, that maybe one day can be an application for the real world. (Imaginary numbers where originally thought of as nothing useful but apparently used in circuitry today under practical application. Bet Descartes would have freaked )

So I hope now, that maybe you can step back and see my side. You, in reality, are correct. I will admit to that (though I dare you to try to find a quote of me refuting that, with respect to reality).

So reality aside, I want to ask you. No explanation is needed, if you say no then I will already understand why you say it. If you were to reach infinity, outside of what we hypothesize to be true in the real world, does 1/∞=0?

the whole .9r = 1 problem has to do with us using base ten...nothing else.

It doesn't prove anything except that some bases are better at representing some numbers.

reply to post by UKLionheart


But no, it is not different. The error for both equations are equal... If one of them can have that error than surely both can

reply to post by PhysicsAdept

Well that is just the thing, it is no paradox... 1 will not equal 2.

Show us how...you can't just declare it.

The math is simple to produce the paradox. Either show a flaw in my math...or prove otherwise that it isn't so.


So let's assume 1/infinity = 0. That would mean 1 = infinity * 0.

But I'm sure you would also say 2/infinity = 0...which would mean 2 = infinity * 0.

Simple replacement gives you 1 = 2.


Show me my error.

Originally posted by OutKast Searcher
reply to post by PhysicsAdept

 

Stop ignoring this

So let's assume 1/infinity = 0. That would mean 1 = infinity * 0.

But I'm sure you would also say 2/infinity = 0...which would mean 2 = infinity * 0.

Simple replacement gives you 1 = 2.

And explain how you resolve this paradox.

Hi. As I said in a previous post, Infinity is a concept, not a specific value, so you cannot perform calculations with it. This isn't a paradox; what ypu have asked is (in maths terms) nonsense. :-(

reply to post by OutKast Searcher


Ooo yeah and let's have a base pi when dealing with geometry and a Plancks base when doing quantum physics, that'll solve everything

Ha I thought we were talking with reality and practicality? Would there not still be problems with other bases? Shall we run away from every discrepancy we find?

Originally posted by UKLionheart

Originally posted by OutKast Searcher
reply to post by PhysicsAdept

 

Stop ignoring this

So let's assume 1/infinity = 0. That would mean 1 = infinity * 0.

But I'm sure you would also say 2/infinity = 0...which would mean 2 = infinity * 0.

Simple replacement gives you 1 = 2.

And explain how you resolve this paradox.

Hi. As I said in a previous post, Infinity is a cincept, not a specific value, so you cannot perform calculations with it. This isn't a paradox; what ypu have asked is (in maths terms) nonsense. :-(

I'm fully aware of all of this.

But since the OP wants to use infinity as a number, I'm showing him how it fails.

The OP claims that 1/infinity = 0.

I disagree with that completely because you can't use infinity in an equation as a number. BUT if he insists on doing so...I'm showing him how it fails.

He ignores it because he can't explain it without admitting that 1/infinity does not equal zero.

Originally posted by PhysicsAdept
reply to post by OutKast Searcher

 

Ooo yeah and let's have a base pi when dealing with geometry and a Plancks base when doing quantum physics, that'll solve everything

Ha I thought we were talking with reality and practicality? Would there not still be problems with other bases? Shall we run away from every discrepancy we find?

We've been through all this.

.9r = 1 comes from the problem of 1/3 = .3r

In base 3, 1/3 (base 10) is 1/10 (base 3), which is 0.1 (base 3).

0.3r (base 10) = 0.1 (base 3).

Here try looking at it like this, I gave ti some thought last night

1/∞= >1,1,0,

Originally posted by OutKast Searcher
the whole .9r = 1 problem has to do with us using base ten...nothing else.

It doesn't prove anything except that some bases are better at representing some numbers.

Sorry, I disagree with this. In base 4:

1, 2, 3, 10, 11, 12, 13, 20 etc.

x = 0.3333333......

multiply both by 4:

10 x = 3.33333....

deduct x

3x = 3

x = 1

0.333333.... = 1 in Base 4.

once again: Tralahhhhh!

double post

reply to post by WhatAreThey


Yep, thats the classic, each step you take is 1/2 the distance of the last, the door might as well be infinitely far away. You will never reach it.

reply to post by OutKast Searcher


Yes but the method you claim to be "more correct" (and now you suddenly disagree that you even [agreed with it ever) has the same error. if 1/∞=.0r1, then 2/∞=.0r1 so then 1 would equal 2.

Have you ever heard the theory of the plane of infinity? Where parallel lines start intersecting with each other? Surely I am not the only one to hear it before. I heard it at a math competition as a speech from the professor, so it wasn't some quack on the streets. He learned from the same books you preach!

As for infinity, if you divide numbers to get 0, who says you are allowed to reverse the operation? Once you take something of value and dissociate it into nothing, does that merit it the capability of being put back together? You gotta then stick with the rules put into place by 0. Anything times 0 is 0... Or you would need to denote some form of ∞ in which when you multiplied it back you would get your original product--which I disagree with!

I am not claiming to know the answers here, I want everyone to explore them so we can find the answers! You can turn it back on me all you want, you are still missing a bit of the point. I dare not reiterate it at the cost of yet again being ignored.

reply to post by OutKast Searcher


I'm sorry; I didn't realise! Hahaha!

The lesson for me today is to read the middle pages of the threads!

reply to post by jb1958


infinitely far away, which means once you travel for a period of infinity, you would get there? Come on guys don't lose focus of the one question that no one has really answered yet.

reply to post by PhysicsAdept

Yes but the method you claim to be "more correct" (and now you suddenly disagree that you even [agreed with it ever) has the same error. if 1/∞=.0r1, then 2/∞=.0r1 so then 1 would equal 2.

I have never agreed that 1/infinity = 0.0r1

I have always said it is undefined.



And you have still ignored the problem...says a lot about you.