Limits at Infinity, the number 1 is bigger than you may think

reply to post by metamagic

2. The stuff about z-scores and variance measures is gibberish. A z score is used to transform an arbitrary NORMAL distribution to a standard normal distribution mean mean=1 and s.d. = 1.

No, the z-score allows you to compare how something relates to something else, the weight of an apple compared to other weights below a normal curve vs. the the diameter of an apple compared to other diameters below a normal curve.

It's not beside the point, it IS your point. You are assuming a normal distribution.

That is not my point, and how would you ever be able to tell me otherwise? My point is not within the actual apples themselves and the comparative figures we speak of them... My OP has to do with the infinite aspect of the number spectrum. My example of apples was to help explain the inaccuracy of a numerical system, when applied to units. Where is the problem here?

reply to post by OutKast Searcher

I disagree with all three of your points

Wow, what a HUGE surprise. Yet, every time I rebuttal any of your posts, you ignore me.... beside the point...

A unit is not a generalization...it is a unit. You apple example is just flat out wrong...because no one says I have 3 perfect apples...they just have 3 apples. The "normalcy" of the apple doesn't matter...all that matters is that it fits the minimum definition of an "apple"...which is not mathematical at all. Same thing if you are counting cars, or clouds, or basketballs. A better example for you to have used is units of measurment...because there is no exact "inch" or "centimeter". So you could argue that something is never exactly an "inch" long...but you can't say you can never have exactly 3 apples. You could say you can never have 3 "perfect apples" as defined by size, color, smoothness, luster, taste, nutritional value, etc. But just using the generic unit of "apple" has not other mathematical criteria rather than the fruit you are counting to be defined as an "apple".

Wait a sec, you are saying already that you disagree with it being a generalization because... wait, because "no one says I have three perfect apples"? CORRECT, no one is not! They are generalizing that you have apples. The apples you would then hold in your hand, all three of them would be different. You are generalizing them by specifically suggesting they are the same in concept. If you told me those apples were all exactly the same, that would not be a generalization now would it? It would be saying that they are all the same. The math comes into play here, because it is nearly impossible to say that they are all the same, each one will have a flaw that another one will not or that will be flawed differently. So instead, you generalize them. You say that you have three apples, and imply that "minimum definition of an "apple"". Don't even try to refute this... you agree with me without even understanding why, you just want to argue...

Each data point does not have an area of zero. It has an area that approaches zero...but it is never zero. It can have an area of 1 if you use some imaginary unit of measure that signifies a very very small area. Or it can have an area of 10^-1000000000000000000000 mm^2. But it will never ever have an area of zero. If you divide into infinite points, than the area of each one could be described as the inverse of infinity...or you can say it is infinitely small...but not zero.

Maybe you have taken an advanced math class, but here would prove to me that you have not. in math, a basic concept is that when you take a limit of something, 1/infinity is equal to 0. Now, do not hit the reply button just yet. I am not just loosely making that assumption. I understand very well that there is some infinitesimal spec left over from that division, but I wonder how much you know about it. What happens when you take the summation as n approaches infinity of 1/n, starting when n=1? You get infinity. In lame-man's terms, you add up a bunch of (p/qs as metamagic) pointed out, and you get infinity. Even though that graph will eventually converge to zero mathematically, the addition of all the parts will end up being an infinite number. An interesting way to prove this, is to take the integration of 1/n with respect to n, from 1 to infinity. What do you get, but the ln(x) evaluated from 1 to infinity, which ends up equaling infinity minus 1, or infinity.

SO I just proved that you are correct using basic calculus, yet here is where even this logic can not make any sense. You do know that there are an infinite amount of points in that circle right? So I broadly stated that you add up a bunch of zero an infinitely large amount of times to get pi, correct? So now, you are reminding us that we actually are adding up more than zero an infinite number of times? So now it looks like my point of this whole thread has been reached! You end up getting a pi unit of infinity! Thanks!

Infinity is a concept. The "infinity" between 1 and 2 is the same as the "infinity" between 1 and infinity. That is why infinity is a concept and not a number. When you start saying one is larger than the other, you are changing the definition.

Sigh... perhaps you should just reread my post. You seem to have gotten nothing out of what has been said. I will just do what you do in a majority of your posts and say, prove it.

Not trying to be mean, really I apologize if I am coming off that way. I merely wish for things to be carefully understood before posting. I get that I suck at getting out what I am trying to say, but now you have to math. Research it all you want--you will find out that I am not wrong numerically

reply to post by metamagic

What do you mean by perfect? In fact you seem to be saying that graphs are close approximations ("the closest you will ever get to a circle that equals pi" -- although it makes no sense to say that a circle equals pi). I would argue that graphs are horrible imperfect. A line has no width yet any depiction of a line has width.. imperfect by my definition.

False, the graph may draw the line, but the graph itself is showing only what you would perceive it to be. When that stuff happens in nature, it only happens as concept, as nothing in nature is truly 2-dimensional. However, rates CAN be. You cannot SEE the thickness of a rate can you? Yet, the graph will show thickness to it, zoom it, I dare you to tell me that line gets thicker.

No reference to Euler's formula at all.

Bull! The only reason why you can call e and pi real numbers are because of his formula, e^(pi*i)+1=0 !

Which is pretty much a total misunderstanding of what a limit and number are. My suggestion is that if you want to publicly use mathematical terms and concepts, take the time to learn what they are. It's actually very interesting.

disprove it, go ahead. How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.

reply to post by IblisLucifer


Very interesting, I like that philosophical approach. So it seems you would agree that the radius of one in which we live, is infinite in ever direction? Haha, not trying to twist your words. This thread seems to have done more damage than imaginative prodding. No one wishes to understand is how I feel, yet in reality I see that everyone does understand, and agrees, that is frustrating. I would say that it is +1 that everyone here knows what is going on, -1 that everyone understands what is going on, and 0 that it is agreed upon.

reply to post by PhysicsAdept

Wait a sec, you are saying already that you disagree with it being a generalization because... wait, because "no one says I have three perfect apples"? CORRECT, no one is not! They are generalizing that you have apples. The apples you would then hold in your hand, all three of them would be different. You are generalizing them by specifically suggesting they are the same in concept. If you told me those apples were all exactly the same, that would not be a generalization now would it? It would be saying that they are all the same. The math comes into play here, because it is nearly impossible to say that they are all the same, each one will have a flaw that another one will not or that will be flawed differently. So instead, you generalize them. You say that you have three apples, and imply that "minimum definition of an "apple"". Don't even try to refute this... you agree with me without even understanding why, you just want to argue...

You are a classic case of overthinking. You have over analyzed this so much that you are saying an apple isn't really an apple.

You are trying to apply mathmatical principles to things that don't require mathematical principles. It's an apple...don't overthink it.

I don't care if I have a perfect apple...no one cares...we define an apple as a certain fruit coming from a certain tree. That's it...no one cares about the "perfect apple".

You are attempting to baffle with BS.

Maybe you have taken an advanced math class, but here would prove to me that you have not. in math, a basic concept is that when you take a limit of something, 1/infinity is equal to 0.

1/infinity is not defined. If you take the limit of 1/x for x approaching infinity, then it approaches zero...it never is equal to zero.

You can try to insult me all you want about my "advanced math classes"...but you are just spouting off things that are not correct.

SO I just proved that you are correct using basic calculus, yet here is where even this logic can not make any sense. You do know that there are an infinite amount of points in that circle right? So I broadly stated that you add up a bunch of zero an infinitely large amount of times to get pi, correct? So now, you are reminding us that we actually are adding up more than zero an infinite number of times? So now it looks like my point of this whole thread has been reached! You end up getting a pi unit of infinity! Thanks!

You continue to use infinity as a number, which to me suggest you don't fully understand it.

In the way you are using infinity...the infinite number of points we are adding have an area of 1/infinity of the whole.

So if you MUST continue to treat infinity as a number...it still doesn't matter. So you start with pi....and divide it by two. You now have two parts that have an area of pi/2...add them up...you have pi. So divide it by 3...you now have 3 parts that have an area of pi/3...add them up...you have pi. So lets divide it up infinte amount of times...you now have infinite parts with an area of pi/infinity...add them up...you have pi.

You are overthinking and confusing the concept for a number.

I feel like you are right in the middle of taking these high level courses and you are confusing yourself.

Sigh... perhaps you should just reread my post. You seem to have gotten nothing out of what has been said. I will just do what you do in a majority of your posts and say, prove it.

I get that you are trying to use infinity as a number instead of a concept. Which is why you are trying to apply mathematical operations to it such as InfinityA > infinityB. And it is just wrong.

Not trying to be mean, really I apologize if I am coming off that way. I merely wish for things to be carefully understood before posting. I get that I suck at getting out what I am trying to say, but now you have to math. Research it all you want--you will find out that I am not wrong numerically

The entire problem is that you are thinking of infinity numerically....you have started off wrong...and so all your conclusions after that are wrong.

reply to post by PhysicsAdept

How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.

Again, you are starting off completly wrong.

You have like half of a concept and are applying it to everything.

I feel like you are thinking in fractals and trying to apply it to everything...and it just isn't right.

You can't tell the exact length of a string in real life...you can never know the exact area of a circle in real life...but you can in concept.

But you can know you have 1 apple. You may not be able to know you have a specific weight of an apple...but you have 1 apple because we have defined an apple to mean something that is only dependent on a few specific details.

Even using your concept of a "perfect apple"...you either have it or you don't. You can't have half of a "perfect apple". You can say that about half of a particular apple meets the definition of perfect...but since it doesn't completely meet the criteria...it is not a "perfect apple".

So your idea of 1 apple not really being one apple...but it is 0.999999999 of an apple just doesn't make logical or mathematical sense.


Again...you are overthinking to the point of confusing yourself.

Originally posted by OutKast Searcher
reply to post by PhysicsAdept

 

How is a number not a limit in and of itself? Because there can never exist perfection in nature that accurately resembles itself as being EXACTLY 1, when we use the number 1 we are referring to the approximation, or generalization of its value. In all likelihood, 1 in nature would really compute to a value of 1.000000000000000000000000000001 in whatever we were determining... You guys really are not getting this post. Confusedly too, seeing as you are obviously very intelligent.

You can't tell the exact length of a string in real life...you can never know the exact area of a circle in real life...but you can in concept.

But you can know you have 1 apple. You may not be able to know you have a specific weight of an apple...but you have 1 apple because we have defined an apple to mean something that is only dependent on a few specific details.

I would like to begin by saying that you have contradicted yourself here. you are saying that you see 1 apple because you have grown up with the CONCEPT of it being one apple but he is wrong because his CONCEPT of one apple is not exactly 1 because his math (statistics) , which is what he grew up with, tells him otherwise. You are saying that concepts are bad because your concept disagrees with it, correct? And you are saying you can find all of these things in concept, such as the area of a circle, but he is not allowed to find infinity as a number IN CONCEPT? If you are going to constantly tell someone they are wrong, and you give an example of their 'error', do not use the same error in your next post.

Just to try and bring the heat down in here a bit....

I'm a non mathematician. Did econometrics and stats at uni.

I just wanted to say how much I am enjoying this thread.

It's awakening a little bit of my brain that was asleep.

Thanks op.

Interesting post, isn't this problem with infinities part of the reason why Chaitin, Wolfram, Wheeler et al argued for digital physics, since there are no large real numbers in nature? A number of paradoxes fall away in this case (though the theory isn't without its own problems).

I have studied this for s few years. One of our assignments have been to find and explain the exact distance between 1 and Zero, And compare and explain that distance to the exact distance between Zero and 1.

Both theoretically and mathematically both should give you the exact same distance. But they don't.

Only from one observation point will you be able to observe and explain the exact distance. From the other observation point, you will not be able to observe or explain the exact distance. You would have to use a symbol to explain.

How can i explain this?

If you have a graph; x, y, z. You have predetermined observation points between Zero and 1. In other words you have chosen a scale with specific values to explain the distance between Zero and 1.

Now, What happened if you take away the graph "the predetermined observation points between Zero and 1" ?

Would the distance between Zero and 1 change? What is now the exact distance between Zero and 1 when you have taken away the graph?

I find Infinities very intriguing. Although in themselves they are only theoretical.

In the real world, they do not and cannot exist. Right ?

Originally posted by Riakennor
I find Infinities very intriguing. Although in themselves they are only theoretical.

In the real world, they do not and cannot exist. Right ?

edit on 17-3-2012 by Riakennor because: (no reason given)

That's certainly my take on the issue. My understanding is that if reality is not granular or discrete, then there would be an infinite amount of information between any two points.

reply to post by ChemistryAdept


It's a bit funny ain't it? He sits there and tells me that no one cares about the perfect apple and that we just group all apples into what tree they came from and then he goes on to tell me that a unit (here the unit is apple) is not a generalization itself. What else is he going to tell me, zero isn't zero--oh but wait, zero is.

Wait a tick... he did do that...

1/infinity (limit- wise) approaches zero. Now, we keep talking about infinity. Some people here would argue that I speak of it as a number, I will not disagree with that here (though I merely believe it should be looked at as a plane, not a number itself.) but, you cannot refer to an infinity as a concept and then argue that 1/infinity does not equal zero. Because in concept, it very realistically will...

Am I truly overthinking this? I thought I brought common sense into discussion. Thinking is a byproduct of discovery, perhaps some people on this thread have not yet discovered their own minds enough

reply to post by selfharmonise


Very good, that gives me hope

Math for me is like the coffee every morning for that little part of the brain.

So what do you think about this mess? Do you see where I am going, with some infinities being bigger than others?

reply to post by Riakennor


reply to post by AlienAnthropologist


Well I believe that we use infinity. If I told you to count particles in the universe, you may think of a million, or total photons the sun has radiated from its birth and you would say it is such a large number that really it is infinite. The truth is, everything that exists, pretty much, can be calculated. Humans put labels on things they cannot, or rather are afraid, count. Infinity exists all over the place in math though. And when it does, I feel it is important to distinguish between all the different "types of infinity". Because as I have said, there are some infinities that are just much larger than others (in concept).

Originally posted by PhysicsAdept

If I told you to count particles in the universe, you may think of a million, or total photons the sun has radiated from its birth and you would say it is such a large number that really it is infinite.

Certainly a very large number undoubtedly, but most definitely not infinite by any means. I don't think you can categorise any number as being approximately equal to or close to infinity.

Originally posted by PhysicsAdept

as I have said, there are some infinities that are just much larger than others (in concept)

I'm glad you added (in concept) at the end there

The problem is, in order to have multiple sizes of infinities, or infinities within infinities. We would have to live in an Infinite universe.

If we live in a Finite universe (which is my belief), it's just not possible to have multiple infinities, or any infinities at all for that matter.

Perhaps if one could fully and accurately calculate infinity and it's place within Mathematics, it would almost certainly give us a lot of answers to questions we currently cannot explain about the universe we live in.

Maybe one day, a new mathematic formula still undiscovered can bring new light on the whole phenomena.

reply to post by Riakennor

The truth is, everything that exists, pretty much, can be calculated. Humans put labels on things they cannot, or rather are afraid, count.

Just makin sure you read this part of my post, I agree with you

And I think that I, as well, believe in a finite universe. It makes much more sense that way, honestly. But, I was hoping people would realize that infinity has different faces. Many people imagine infinity to be some gigantic, incomprehensible number. But, let us not forget of the infinite amount of points that a unit circle can have. Even if we had a true sphere, with radius of 1-meter, it (might) exist in space under an infinite amount of points, just as on paper with a circle. So then we have a a body, or "system" of 4pi/3 meters^3, which is an finite number of points in space. This system, however, is much less than a sphere of say 100 meters radius. It also has perhaps an infinite amount of points in space, yet obviously many more points than with radius of 1.

See where I am going?


ETA: Not to say, of course, that that sphere holds infinite mass, which I believe is what you are specifically speaking of. We all know that sphere does not hold infinite mass.

Originally posted by PhysicsAdept
Even if we had a true sphere, with radius of 1-meter, it (might) exist in space under an infinite amount of points, just as on paper with a circle. So then we have a a body, or "system" of 4pi/3 meters^3, which is an finite number of points in space. This system, however, is much less than a sphere of say 100 meters radius. It also has perhaps an infinite amount of points in space, yet obviously many more points than with radius of 1.

See where I am going?

For sure I see where you're going and to some extent makes sense. The problem is you can't logically say (not that we live in a logical universe, but that's another discussion ) that there's less infinite points in one sphere, than there are in the larger sphere.

Infinity never ends so it's impossible to make the calculation or the assumption that the larger sphere contains more infinite points.

Infinity + any other number or any other numbers of infinities.. or even if you will, an infinite number of infinities x infinity = Infinity.

You really cannot place boundaries around infinity.

My brain hurts, I hope it makes sense

reply to post by Riakennor


Very true, I suppose we only slightly disagree. Then again, as you pointed out, what in this world holds true logic?