Infinity is.....

[geko]

Didn't really know what title to give as you can tell from the dots... but it's about infinity, obviously. I thought maybe 'infinity doesn't exist', but that wasn't quite right, so what better way than to just start rambling...

 

I just finished watching a documentary on infinity, and in it, like so many other pieces on infinity, they go about trying to delve into the mysteries of infinity, highlighting why it's a strange and abstract idea. Several examples given, but 1 of which was the idea that if you string numbers together 1 > infinity, then take out only the even numbers and put that list alongside the first both lists are the same length even though list 2 has only half the numbers.

 

Aye, boggling stuff.... and there were other examples, but it doesn't matter as i'm here to tell you it's not boggling. It's easy. It doesn't confuse and isn't mysterious. In fact, it requires only a couple of sips of coffee to get your head around!

 

Bare with me.... as here's my argument. (which is bulletproof... completely and utterly, armour pierced, laser guided, skud sized tomahawk bazooka missile style proof!... whatever).

 

The problem with people's ability to understand infinity is quantity. It doesn't have one. It isn't one. It's a concept, not an amount.

 

That is all.

 

Sure, this isn't a radical idea, and maybe it's what people actually see infinity as.... but if that's so i'm confused as to why whenever infinity is spoken about it's highly likely someone will try to help you understand the conception by inserting a quantity, and therefore a perspective. It's the wrong way to go about things.

 

Infinity + 1 is meaningless. The idea itself is spurious since you can't add a number to a concept that exists independent of quantity. It's non-sensical... and just for the rhetoric i'm sure it's in the same realm as what's north of the north pole and how much time passed before time began....

 

So for the sake of redundancy, infinity means 'forever'. Using the concept of infinity to describe something in existence doesn't necessarily mean, irrespective of whether or not the object related to could have a characteristic measurement, that a quantity has to be invoked. For example, the assertion that 'the universe is infinite' cannot therefore be proceeded by 'so how many metres is that?' The question is stupid.

 

I know it might not sound special, but i swear this solves problems! Never again do i wish to see someone try and conceptualise 'the amount' that is infinity. No more quantity with infinity, it's superfluous.

 

Please, argue with me, i welcome the debunking of my reasoning :)

[sanctus]

Moved it to philosophy of science, thought it fits much better here. Contact me or any other staff if you feel it should be in another forum.

 

Sandro

[geko]

...thought it fits much better here.

 

Yes, i did think about philosophy forum for it at first, but chose maths as thought it fit better there :) ... but whatever you think's best.

[Pyrotex]

... The problem with people's ability to understand infinity is quantity. It doesn't have one. It isn't one. It's a concept, not an amount. ...Please, argue with me, i welcome the debunking of my reasoning :)

Hmmm...

 

I'm sorry, dude, but I make it a point to never argue with someone who is dead-on correct.

 

Maybe it's just me, but debunking a FACT has always bothered me a little. :)

 

And the FACT is, you are right. And most folks just cannot get it.

 

Congratulations!!! You got it.

 

:doh: :) :eek: :shrug: :thumbs_up :doh:

[geko]

Really? I admit i'm a little bemused! Why do people always stick a quantity on it i ask....

 

I was thinking i actually thought of something so simple yet it escaped everyone... ho hum... still, hopefully i have many years left to realise something at least a little profound... :)

[Rade]

Hi Geko,

 

Your reasoning matches very well that of Aristotle, which he wrote 2000+ years ago, in his writings called the "Physics". His discussion of the concept "infinite" begins in Book III, Chapter 3 of "Physics".

 

He is some of what he has to say about the "infinite":

 

1. There cannot be a source or limitless of the infinite, for that would then be a limit of it.

2. Given that the infinite is a beginning, it is both uncreatable and indestructible.

3. There is no body that is actually infinite

4. When we speak of the actual existence of a thing (such as a statue), we mean there will be an actual statue. But it is not so of the infinite, there will not be an actual infinite.

5. The infinite exhibits itself in many ways, in time, in the division of magnitudes.

6. The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, but what always has something outside it.

7. Our definition of the "infinite" then is as follows: A quantity is infinite if it is such that we can always take a part outside what has been already taken. [On the other hand, what has nothing outside it is complete and whole].

 

So, my only argument with your post is your statement that "infinity means 'forever". Given that it is logically possible to suggest that a "whole" to be "forever", and if we accept the definition of Aristotle that the "whole" is the contrary of what is "infinite", then it must follow that infinity does not mean forever. Better imo to say "infinity means beginning".

 

Well, this is how I see it--nice post.

[Turtle]

Didn't really know what title to give as you can tell from the dots... but it's about infinity, obviously. I thought maybe 'infinity doesn't exist', but that wasn't quite right, so what better way than to just start rambling...

 

I just finished watching a documentary on infinity, and in it, like so many other pieces on infinity, they go about trying to delve into the mysteries of infinity, highlighting why it's a strange and abstract idea. Several examples given, but 1 of which was the idea that if you string numbers together 1 > infinity, then take out only the even numbers and put that list alongside the first both lists are the same length even though list 2 has only half the numbers.

...

Please, argue with me, i welcome the debunking of my reasoning :shrug:

 

geko, you're shapin' up to be a hale fellow well met. there's one thing about threads on infinity; you can always add one more. :shrug:

Hypography threads on Infinity

 

the last bit you touch on falls under "countable sets" and as luck has it, i just gave an introductory bit on it in another thread where we are using that concept to qualify some sets under investigation. post #156 :http://hypography.com/forums/physics-and-mathematics/20236-non-figurate-numbers-16.html

 

to infinity and beyond! :lol: :naughty:

[lawcat]

So for the sake of redundancy, infinity means 'forever'.

I think, like Rade, that equating infinity with forever, which is in time, is too narrow.

Using the concept of infinity

I agree that it is a concept, but what kind of concept?

to describe something in existence doesn't necessarily mean, irrespective of whether or not the object related to could have a characteristic measurement, that a quantity has to be invoked. For example, the assertion that 'the universe is infinite' cannot therefore be proceeded by 'so how many metres is that?' The question is stupid.

True because the answer was already given--infinite.

 

Inifinity is a concept of condition. It conditions the object, it tells us something about the object but not about its measurement. Rather it tells us about its boundary condition. It tells us that it is limitless, as opposed to limited. So inifinity is absence of limit, absence of boundary. It is a condition of the boundary regardless of the metric. The boundary is non existent.

 

For example, between number 1 and 2, the quantity is 1 and is not infinite, it is bounded by 1 and 2, it is limited. But the quality of 1 is infinite because there are inifinite many decimal spaces, the decimals have no boundary, and the quality which the quantity 1 between 1 and 2 can take is limitless, infinite.

[geko]

Sorry, i'm not sure why i actually used such a poor term like forever. Guess i wasn't thinking critically. Limitless is what i should have said.

 

....

 

Rade, i must confess i've never read Aristotle. Nor Plato or Socrates. I find the writing style makes it very difficult for me to understand. Of course, i'm not saying it should be easy, as hey, it's philosophy after all; a very difficult subject at the best of times.

 

Bad of me i know. I should read them.

 

Although in my defense i did wade through Hume :shrug: ... but i think that might have been because i found it intuitive and therefore the style easier to follow.

[Boerseun]

...the mirror opposite of 0.

[Yoron]

I've always felt a little uncomfortable with the idea of different 'infinities'. If you assume that the concept is 'infinite', then how can you set a boundary on it. A alternative way would be to see it as not relating to our number logic at all, but to be a concept defining something that you can find everywhere, where you can't define a boundary.. To think that just because you create a number system in where you have an 'infinite' possibility of inserting new numbers between what you define as a logical higher order seems to me a little like numerology.

 

I can see the concept but if a infinity can be of any magnitude + 1 ad infinitum, and yet have a boundary, and you then try to treat it as a 'real world' solution to a problem, then it won't matter how many photons I pour into my tank, will it? As they are able to be superimposed they too contain an infinity it seems to me? And now someone will translate this into vectors of momentum and energy-mass :) but it won't change the basic reasoning I think, unless you then want to design a new theorem proving that infinities always breaks down ::))

 

But I do see the logic presenting as well as counting on larger and smaller 'infinities'.

[Doctordick]

You gentlemen have been mixing two very different things. First, you need to understand the definition of “infinite”. Infinite is a label assigned to the concept that something can not be finished: i.e., no matter how far you go to accomplish the process, you have not finished; that circumstance is call infinite.

 

Now, the second thing you don't seem to understand is the fact that the field of mathematics is design and analysis of internally consistent systems. Anytime one introduces a new concept, mathematicians try to see if they can construct a new internally consistent abstract system making use of that concept. That is where these “different infinities” arise. Clearly there are different processes which satisfy the definition of infinite. The question is, can one fabricate a logic system relating these different processes which is internally consistent. Apparently one can.

 

I personally haven't examined these ideas myself, but I am certainly aware of some rather wild ideas that mathematicians have concerned themselves with. Mathematics as a field is not a closed system. Back when I was a graduate student in physics, I noticed something that no one had ever pointed out to me. In calculus, derivatives are integer in nature: i.e., in in the abstract representation of a derivative

[math]\frac{d^n}{dx^n}f(x)[/math]

 

n is always an integer. I asked myself the question, is it possible to define that operator such that n can be an arbitrary real number. I worked with it for a while and came up with a definition which seemed to be totally internally consistent. I took what I had done to my favorite math professor (who happened to be an old geezer who had gotten his doctorate back in the 1800's; a very knowledgeable man). He looked at it, pushed back from his desk, took a book from the bookshelf and handed it to me without a word. It was a math Ph.D. Thesis on exactly that subject. The point being that mathematicians have done astonishing things which in the final analysis seem to have no use at all. But I am sure they enjoyed the process.

 

Have fun -- Dick

[coldcreation]

[snip]Back when I was a graduate student in physics, I noticed something that no one had ever pointed out to me. In calculus, derivatives are integer in nature: i.e., in in the abstract representation of a derivative

 

[math]\frac{d^n}{dx^n}f(x)[/math]

 

n is always an integer. I asked myself the question, is it possible to define that operator such that n can be an arbitrary real number. I worked with it for a while and came up with a definition which seemed to be totally internally consistent. I took what I had done to my favorite math professor [snip]. He looked at it, pushed back from his desk, took a book from the bookshelf and handed it to me without a word. It was a math Ph.D. Thesis on exactly that subject. The point being that mathematicians have done astonishing things which in the final analysis seem to have no use at all. But I am sure they enjoyed the process.

 

Have fun -- Dick

 

Yea, but the questions is; was the solution or internally consistent definition found in the Thesis the same as yours?

 

I don't mean to kill any cats, but, just out of curiosity, do you recall name of the person who wrote it (or what the title was)?

 

 

CC

[Illiad]

If you divide a 10 m^3 vacumn exactly into 3, what will be the 'volume' of each vacumn?

[Doctordick]

Yea, but the questions is; was the solution or internally consistent definition found in the Thesis the same as yours?

Yes and no. The impression I had at the time was that the professor was simply pointing out to me that “real original work is hard to come by”. That's why “re”-search is so important. As I remember it, the stuff I had come up with was there but he had one hell of a lot more, bringing up issues that never even occurred to me. I only glanced at it but saw enough to convince me that I wasn't in his league. I only mentioned this event because I thought it pointed out an aspect of mathematics we outside the field are completely oblivious of. I suspect the real reason no one knows about it that there seems to be no use for it. It could be little more than an exercise in imagination.

 

And I cannot tell you what his conclusion was concerning internal consistency of the general concept. He could easily have shown it was internally inconsistent. I don't know.

 

That was exactly the problem with my fundamental equation when I first discovered it: though I knew it was true, there seemed to be no use for it.

I don't mean to kill any cats, but, just out of curiosity, do you recall name of the person who wrote it (or what the title was)?

No! We are talking about an event which probably lasted less than five minutes close to fifty years ago. To tell you the truth, I don't even remember the professor's name anymore. I was in physics and imaginative math really wasn't that interesting to me.

 

I had only gotten curious about the issue because myself and some other studentsI had just been talking about idea that logs arose when the possibility of fractional exponents was examined. Originally the exponential notation merely told one how many times to multiply the number by itself and fractional exponents were kind of meaningless.

 

Sometime back in the nineteen seventies I went to show him my fundamental equation thinking he might be able to point we towards some way to find solutions to it and found out he had died.

[Ben]

So inifinity is absence of limit, absence of boundary. It is a condition of the boundary regardless of the metric. The boundary is non existent.

Well, I accept this is a philosophical discussion, not a mathematical one, but nonetheless, I take exception to this; or rather, I can make no sense of it.

 

For example, between number 1 and 2, the quantity is 1 and is not infinite, it is bounded by 1 and 2, it is limited. But the quality of 1 is infinite because there are inifinite many decimal spaces, the decimals have no boundary, and the quality which the quantity 1 between 1 and 2 can take is limitless, infinite.

Which makes no sense to me either. Am I missing something?

 

There is a a bunch of easy theorems out there that show that if [math]\mathbb{R}[/math] is uncountably infinite (it is) then so is the subset [math][0,1]\subsetneq \mathbb{R}[/math]. id est [math][0,1][/math] and [math]\mathbb{R}[/math] have the same cardinality! Weird or what?

 

But the subset [math][0,1][/math] is obviously bounded, so boundedness is is NOT a condition on the cardinality of a set, which in the present case we are assuming, or at at least I so do, is infinite