An infinite number of objects and universes

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Reply Thu 27 May, 2010 01:56 pm
In mathematics, there can be infinite sets in topological space. In one sense, this shows that infinity exists. However, infinity is not itself a number, but a relationship between hypothetical numbers that cannot be finished being counted to. So a mathematical equation, or rubric, can demonstrate infinity, but still does not satisfy the requirements necessary for there to be an infinite amount of actual physical objects. The very question "Is there an infinite amount of" or "Is there an infinite number of" x items actually in existance seems flawed because there cannot be an "infinite number". For there to be an infinite number of things, infinity would have to be a number. However, there is no number itself actually equal to infinity, so infinity is not a number.

For this reason, there cannot be an infinite amount of specific items. There cannot be an infinite number of pink plastic cups. You cannot subtract 1 from infinity and have less, so if there were an infinite amount of pink plastic cups, you could never remove one from existence. You cannot subtract 1 from infinity, because you can only subtract from a number and again, infinity is not a number. I am able to destroy a pink plastic cup causing there to be one less, so it seems to follow that there are not an infinite number of them.

If this is true of pink plastic cups, the same should be true of sentient beings, so there couldn't be an infinite number of "me". Though we have not yet been able to witness or verify the actual destruction of a universe, it still stands to reason to say that a universe can be destroyed as well. Its not certain how a universe would be "destroyed", but perhaps its energy cannot be destroyed, but that the configuration of its energy be so drastically altered or transferred into another universe or state that it no longer qualifies as the same universe. So if all things, including universes, can be subtracted from existence by at least the number 1, and you cannot subtract 1 from infinity, it seems that there cannot be an infinity of objects.
 
TuringEquivalent
 
Reply Thu 27 May, 2010 08:44 pm
@setzer9999,
setzer9999;169669 wrote:
In mathematics, there can be infinite sets in topological space. In one sense, this shows that infinity exists. However, infinity is not itself a number, but a relationship between hypothetical numbers that cannot be finished being counted to. So a mathematical equation, or rubric, can demonstrate infinity, but still does not satisfy the requirements necessary for there to be an infinite amount of actual physical objects. The very question "Is there an infinite amount of" or "Is there an infinite number of" x items actually in existance seems flawed because there cannot be an "infinite number". For there to be an infinite number of things, infinity would have to be a number. However, there is no number itself actually equal to infinity, so infinity is not a number.





Suppose, what we mean by "infinite" are infinite sets! In such a way, a flat-space can be approximated by the set of R "cross" R. Where R is the set of real numbers, and "cross" is Cartesian product.


Similarly, a universe can be isomorphic to an instance of a mathematical structure. Since there infinite many possible mathematical structures, and their instances, then why are there not infinite my universes?


I am sorry if this is a bit abstract, but if you don` t understand, i can say some more. In any case, your assumption 'infinite is not a number' is true, but the modern perspective comes from understanding 'infinite' as sets.
 
setzer9999
 
Reply Fri 28 May, 2010 07:01 am
@TuringEquivalent,
I agree that the math behind infinite sets is logical and correct. The problem I see is that though a set of numbers can converge on infinity, the fact remains that it never "reaches" infinity. In this way, the universe, or all of existence, can converge to infinity, but never reach it. Existence can be said to have no limit, but that's not actually the same thing as being infinite. It is always able to grow, but it can't reach the "height" of its growth potential. So, with unlimited energy and potential, you could hypothetically continue to manufacture pink plastic cups for eternity, but the number of them would still never "reach" infinity. The fact that there is even 1 object that can be counted seems to indicate that there are not an infinity of objects, but an exact number of them, no matter how high that number is.

Equations containing numbers and symbols are good representations of objects, but you can't actually have your equation truly represent infinity in numbers. You demonstrate that the relationship is infinite, for example there is an infinite relationship between even and odd numbers, but you can never actually write down and show an infinite amount of numbers themselves. Relationships can be infinite sets, but it seems the number of objects that exist cannot.
 
TuringEquivalent
 
Reply Fri 28 May, 2010 08:01 am
@setzer9999,
Quote:
I agree that the math behind infinite sets is logical and correct. The problem I see is that though a set of numbers can converge on infinity, the fact remains that it never "reaches" infinity. In this way, the universe, or all of existence, can converge to infinity, but never reach it. Existence can be said to have no limit, but that's not actually the same thing as being infinite.



The approach of looking 'infinite' as sets implies that we use the notion of 'complete infinite', and not the older notion of 'approximate infinite'.
The latter notion is one adopted by newton, and the calculus, while the former is adopted by cantor. In brief, there is no 'approaching infinite'.

Quote:

Equations containing numbers and symbols are good representations of objects, but you can't actually have your equation truly represent infinity in numbers. You demonstrate that the relationship is infinite, for example there is an infinite relationship between even and odd numbers, but you can never actually write down and show an infinite amount of numbers themselves. Relationships can be infinite sets, but it seems the number of objects that exist cannot.



There is no 'infinite number', but there are infinite sets. What is wrong with modeling a possible universe with an infinite set? We can imagine a universe with 2 spatio-dimension. We don ` t need any equations at all. A cartesian product can easily do the job.
 
setzer9999
 
Reply Fri 28 May, 2010 08:38 am
@TuringEquivalent,
This is why I put "reaches" in quotations. Its absurd to think that you can "approach" something that is indefinite. I do agree that a universe can contain elements that can be modeled with infinities. Infinities are even different "sizes" in different sets. This is in relationships, which can only be represented by numbers, but do not actually equal a total number. You can never write down every number in an infinite set. Still there is such a "thing" as infinity. A relationship doesn't necessarily have to have a set number of actual objects, only infinite relationship. "Relationship" is not a discrete object, so this is why a set can be infinite.

However, a group of objects behaves differently than a set in that there is a number of objects. Each object is discrete, or else it would not qualify as being an object. The relationship between any set of these objects might be infinite, but the number of the objects themselves can never "equal" infinity because in order to equal it, it would have to be a definite number.
 
TuringEquivalent
 
Reply Fri 28 May, 2010 09:32 am
@setzer9999,
setzer9999;169974 wrote:
This is why I put "reaches" in quotations. Its absurd to think that you can "approach" something that is indefinite. I do agree that a universe can contain elements that can be modeled with infinities. Infinities are even different "sizes" in different sets. This is in relationships, which can only be represented by numbers, but do not actually equal a total number. You can never write down every number in an infinite set. Still there is such a "thing" as infinity. A relationship doesn't necessarily have to have a set number of actual objects, only infinite relationship. "Relationship" is not a discrete object, so this is why a set can be infinite.

.


what is an "infinite relationship"?


It seems you do agree that we can model a spatially infinite universe
using an infinite set, right? ( all i am saying is that you can)
Quote:


However, a group of objects behaves differently than a set in that there is a number of objects. Each object is discrete, or else it would not qualify as being an object. The relationship between any set of these objects might be infinite, but the number of the objects themselves can never "equal" infinity because in order to equal it, it would have to be a definite number


this makes no sense at all to me. If you have finite many objects, then the collection have a finite size. Eg 2= | { cat, dog}|


What is the relation between any set of {cat, dog}. Give me some examples.

The size of {1, 2, 3,....} is a transfinite number.
 
setzer9999
 
Reply Fri 28 May, 2010 09:48 am
@TuringEquivalent,
I said they "might" be infinite, not that any set of objects "do" have an infinite relationship.

{1, 2, 3 ... } is not a number, its a description of a relationship or property of "ongoingness", but has no actual, ultimate, or specific value. No specific one number is equal to it.
 
TuringEquivalent
 
Reply Fri 28 May, 2010 10:41 am
@setzer9999,
setzer9999;170000 wrote:
I said they "might" be infinite, not that any set of objects "do" have an infinite relationship.


This is not my question. Again, what is "infinite relationship". What the hell is that?


Quote:
{1, 2, 3 ... } is not a number, its a description of a relationship or property of "ongoingness", but has no actual, ultimate, or specific value. No specific one number is equal to it.


It is a mathematical fact that cardinality of the natural numbers {1, 2, 3 ...} is a transfinite number. It is not up to dispute, or discussion. This is part of mainstream theory of infinite sets.


I would avoid using no technical terms like "ongoingness", or "specific value". When we talk about sets, the notion size becomes cardinality. When talk about infinite sets, then we talk about 'complete infinite', and 'transfinite numbers'. It makes on sense to about " ongoingness" of numbers, until you fail to understand the technical language.
 
setzer9999
 
Reply Fri 28 May, 2010 01:06 pm
@TuringEquivalent,
The point isn't what term to use, and the point isn't whether or not you can demonstrate infinity, or infinite sets with math. Using the term "specific value" is perfectly valid. I could just as easily say "specific number" or "specific ammount", the term is irrelevant. The point is that though you can demonstrate infinity through math, you can never have infinite actual objects.

The "infinite relationship" I am refering to is the characteristic of the cardinal set such that 1 is related to 2 the same way that 2 is related to 3 and the same relationship is true of all integers. The only way you demonstrate infinity is by this relationship. You don't actually have a number "infinity", you only have an infinite relationship, otherwise, the statement that the cardinal set is infinite would be impossible.

No matter how much you can demonstrate this, or how many terms you come up with to define it, the very simple fact that you still never have a number equal to infinity remains. Its not a number, so there can't be a number of things equaling it. So there aren't infinite things.
 
TuringEquivalent
 
Reply Fri 28 May, 2010 01:28 pm
@setzer9999,
setzer9999;170062 wrote:
The point isn't what term to use, and the point isn't whether or not you can demonstrate infinity, or infinite sets with math. Using the term "specific value" is perfectly valid. I could just as easily say "specific number" or "specific ammount", the term is irrelevant. The point is that though you can demonstrate infinity through math, you can never have infinite actual objects.

The "infinite relationship" I am refering to is the characteristic of the cardinal set such that 1 is related to 2 the same way that 2 is related to 3 and the same relationship is true of all integers. The only way you demonstrate infinity is by this relationship. You don't actually have a number "infinity", you only have an infinite relationship, otherwise, the statement that the cardinal set is infinite would be impossible.

No matter how much you can demonstrate this, or how many terms you come up with to define it, the very simple fact that you still never have a number equal to infinity remains. Its not a number, so there can't be a number of things equaling it. So there aren't infinite things.



Because it is obvious wrong...


In cosmology, if density is low, and the distribution of matter is evenly distributed, then there are infinite many universes with size of our observable universe. Don` t question this, because it is a fact. I can give you reference to support it.

If this is indeed the case, then it is part of a mathematical theory. This theory is mathematical is a model of the universe. Don` t this mathematical model, models infinite many things? Yes.
 
setzer9999
 
Reply Fri 28 May, 2010 01:51 pm
@TuringEquivalent,
I disagree that anything about the nature of the infinite is obvious, wrong or right.

In cosmology, the density of a universe dictates, in part, the radius of the curvature of that universe, not the number of universes. Again, being infinite is a characteristic that exists in some contexts.

A number cannot have the characteristic of being infinite. Infinity is not a number. So you can't say you have "infinitely many universes" because that is quite literally another way of saying "an infinite number of universes", which is a contradition in terms.

You can indeed model some characteristics with infinities including some characteristics of the universe itself. The number of objects that exist is not one of these.
 
TuringEquivalent
 
Reply Fri 28 May, 2010 03:31 pm
@setzer9999,
setzer9999;170083 wrote:
I disagree that anything about the nature of the infinite is obvious, wrong or right.

In cosmology, the density of a universe dictates, in part, the radius of the curvature of that universe, not the number of universes. Again, being infinite is a characteristic that exists in some contexts.

A number cannot have the characteristic of being infinite. Infinity is not a number. So you can't say you have "infinitely many universes" because that is quite literally another way of saying "an infinite number of universes", which is a contradition in terms.

You can indeed model some characteristics with infinities including some characteristics of the universe itself. The number objects that exist is not one of these.



No! The density, and distribute don` t determined any "radius". The universe is much "larger". The observable universe is a volume determined by the radius of how much time light travel from the big bang to how far we can see. That is traditionally know as the "observable universe". There is still space beyond that.

The consequence of the geometry of the universe( the whole thing), and the distribute of matter is evenly distributed, then every possible configuration of matter is realized in an "infinite" amount of times. Why are you doubting this? This is the standard theory. I can give you references for it.


If you question the mainstream theory, then i have nothing to say to you. The discussion will longer be productive for me.
 
setzer9999
 
Reply Sat 29 May, 2010 06:51 am
@TuringEquivalent,
If it is the mainstream theory that the universe has an "infinite amount" of configurations actually present, not the infinite potential for configuration, then yes I decent. Potential can be infinite, the number of configurations that actually are cannot.

Being infinite is a characteristic only a singluar continuum (such as potential, relationship, etc) can have. You can't have "infinite many" or "infinite amount" because "many" and "ammount" imply a number. You can't determine the number of the "last" universe configuration counted in this model. Infinity is unreachable as a number of objects.

Mathematics may be able to model infinities, but this doesn't mean the universe itself is infinite. Mathematics also models zero, but the universe is not nothing. I am aware that the concept of the number 0 is not nothing, its the presence of an absence, but actually having zero objects in existence would equate to there being nothing whatsoever (which is another thread, and I pose that this too is impossible).

I will have to use phrases that are contradictions in terms for this next part since our language is limited to what is logical and possible and I'm attempting to describe nonsense. If there were infinite configurations of the universe, there would be infinitely many configurations of the universe that cause all other configurations of the universe to be impossible. The only way the universe can be infinite is if the "sum" of all of these cancelations boils down to a finite set... thereby making it not infinite.
 
ughaibu
 
Reply Sat 29 May, 2010 07:36 am
@setzer9999,
setzer9999;170333 wrote:
You can't have "infinite many" or "infinite amount" because "many" and "ammount" imply a number.
Are you suggesting that reality is defined by a particular lexicon?
 
setzer9999
 
Reply Sat 29 May, 2010 07:44 am
@ughaibu,
I was wondering when someone was going to ask this question. No. The lexicon does not govern reality, it is the other way around. Our language is part of reality, and a way to describe realtiy. The word "number" does not govern the characteristics of the universe, but is simply our way of communicating to one another that the object being refered to has the characterisitic of being a number.
 
ughaibu
 
Reply Sat 29 May, 2010 07:57 am
@setzer9999,
setzer9999;170344 wrote:
I was wondering when someone was going to ask this question. No. The lexicon does not govern reality, it is the other way around. Our language is part of reality, and a way to describe realtiy. The word "number" does not govern the characteristics of the universe, but is simply our way of communicating to one another that the object being refered to has the characterisitic of being a number.
Okay, then we cant dismiss the possibility of there being an infinity of objects on the grounds that terms, such as many and amount, are (considered by some to be) finitary.
 
setzer9999
 
Reply Sat 29 May, 2010 08:41 am
@ughaibu,
Infinity appears to not have a characteristic of a number being that a number has to be definite. However, let's assume that on this I am mistaken. Let's treat infinity like we treat specific numbers.

If the configurations are infinite, then there are no configurations that are not. As such, every configuration that would preclude the possibility of another configuration also exists. If a "Universe 1" exists, but we have infinite universes, another universe, "Universe 1b" that has the properties of being able to negate the conditions necessary for "Universe 1" to exist. Perhaps it has the property such that somewhere within itself a singularity so hot emerges that it punctures Universe 1 and absorbs its mass before it can exist. Perhaps it contains powerful beings that can navigate higher dimensions and they destroy the other universe. The exact nature of this interaction is irrelevant. The point is, that if you have infinite things, then there is nothing that isn't, including things that make other things not be. You can substitue universes for objects within a universe too. If there are infinite objects in a universe, then there exists an object that precludes the existence for each object.

However, this is not subtraction. The Universe 1b is not the "negative" of Universe 1, it is an existant universe that has the properties of causing Universe 1 to not be. To demonstrate this, we find the average, not the difference. To do this:

∞/∞=1

In treating infinity as a number, the total number of universes is 1. I realize that infinity divided by itself is NOT equal to 1, I'm just saying if we're going to treat it as though it is a number things can be equal to, it would. Any number something can be equal to divided by itself is 1. Really, ∞/∞ is an indefinite value... it is undefined.

I also say this whole line of thinking seems nonsense, because Universe 1b would also have a Universe 1b_b which would preclude its existence. However, if this all COULD happen "simultaneously" and infinity be a number of things, the average is still 1, not infinity.

It seems to me that the number of universes is somewhere between 1 and a really high number, but that high number is not infinity.
 
ughaibu
 
Reply Sat 29 May, 2010 08:43 am
@setzer9999,
setzer9999;170358 wrote:
If the configurations are infinite, then there are no configurations that are not.
What does this mean and how do you support it?
 
setzer9999
 
Reply Sat 29 May, 2010 08:49 am
@ughaibu,
If the configurations are infinite, you cannot have one less than infinity. Even if we treat infinity like other numbers, where we can say ∞/∞=1, we cannot say ∞-1 = undefined.

We are saying that ∞ is to be treated like a defined number, but yet we cannot even define what one less than it is. So, you can't exclude even one configuration that destroys another, because to do so you would have to subtract 1 from infinity, which is impossible.

This is why the whole idea that there are infinite configurations is absurd. In a sense, you are asking me to support something that is demonstrating its own impossibility.
 
ughaibu
 
Reply Sat 29 May, 2010 08:53 am
@setzer9999,
setzer9999;170362 wrote:
If the configurations are infinite, you cannot have one less than infinity.
I've no idea what you mean. If there is a system of natural numbers, with addition, then there is singularity and infinity. How does infinity disable finitude?
 
 

 
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