Dealing with Infinity: Exploring Theories of Boundless Questions

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In summary, the concept of infinity poses a major problem in understanding the limits of the universe, particularly in the context of the multiverse and theories like brane theory and black hole-white hole theory. While there are many theories, the issue of infinity remains a common thread. The idea of studying singularities and their nature is also closely related to understanding infinity. In regards to our own universe, there is still debate over whether it is finite or infinite, but its age and expansion rate suggest it is finite. However, there may still be unseen boundaries and unexplored regions beyond what we can currently observe. Ultimately, the concept of infinity remains a complex and ongoing topic of study.
  • #1
osxraider
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How do we deal with the concept on infinity? It seems to linger about the limits of everything.

For me, this is the biggest problem in some sense. I wanted to ask the question in the context of the the multiverse. This is a big trend now in physics and cosmology and usually gets lots of people excited

Since we have now started saying that our Universe might not be the only one, haven't we simply pushed up the problem into a higher category. Let's just imagine that the Universe is a finite soap bubble and so as in common analogy, there are many bubbles/universes in the multiverse but if I ask whether all these bubbles are in finite bath tub? then the answer is equivalent to saying that our single Universe is infinite.

Suppose we did start saying that someday that our Multiverse is also a finite one, a really big bubble with lots of bubbles in it which share some common properties (superset, subset), then there would suddenly be the multi-multi verse! So really at this point, aren't we just pushing infinity higher and higher to avoid dealing with it?

Now suppose we take the brane theory and there are all these parallel branes stacked and they touch every once in a while creating big bangs, well these branes are supposed to stretch infinitely so where would they touch? Not to mention, there is an infinite stack of these membranes.

Then there is the black hole-white hole theory. Ok, some our Universe might be in a black hole opening into another realm the opposite side of which is a white hole and we see it as the big bang. So its like branching since we know lots of black holes are there in our Universe. Where then does the first black hole com from?

Of course, there are many theories but this infinity thing runs as a common thread. For me, dealing with infinity is the same as studying a black hole. The gravitational singularity comes into play right at the start of our Universe and we encounter the same thing at the center of black holes.

Why aren't we all just working on figuring out what happens at singularities. At this point we're pretty sure that black holes DO exist but how is infinite density possible/zero volume possible? What is its nature? Can it be described definitely rather than in infinite terms?

if something falls towards a singularity, what happens to it? does it emerge elsewhere in another form? We we could know, wouldn't we automatically know how things can come out of singularities like out Universe?

Is there a conceivable limit to what we can know and answer quantitatively and qualitatively?

Also, just a side question about our Universe itself? Isn't it supposed to have finite matter/energy? and there is a definite rate of expansion so it must be finite in the sense that it has only stretched so much? also, it has a definite age so it seems like that itself must impose a limit/boundary. I'm not hinting towards the sort of thing where I then ask what exists outside this boundary? I've seen posts before that asked this question and it was frowned upon but is there a distance from our point of view in every direction where the Universe has still not expanded to?

The CMBR should not exist at a certain point or rather, there should be a point where there is no temperature.
 
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  • #2
osxraider said:
Is there a conceivable limit to what we can know and answer quantitatively and qualitatively?

There could be. We can try, and if after a million or so years there is no progress then I would be tempted to give up. But those in search of a PhD will still find something to write about, I suppose.

Also, just a side question about our Universe itself? Isn't it supposed to have finite matter/energy?

If the Universe is finite then it has finite matter and energy.
If the Universe is infinite and homogeneous then it has infinite matter and energy.
and there is a definite rate of expansion so it must be finite in the sense that it has only stretched so much?

It could have been infinite at creation in which case it is still infinite.
It could have been finite at creation in which case it is still finite and will very likely always be so.

also, it has a definite age so it seems like that itself must impose a limit/boundary. I'm not hinting towards the sort of thing where I then ask what exists outside this boundary?

The future exists outside of the boundary of the Universe's age. There is also a limit as to how far we can see with telescopes, that's called the visible universe. Beyond the visible universe is the transvisible universe, I guess.

I've seen posts before that asked this question and it was frowned upon but is there a distance from our point of view in every direction where the Universe has still not expanded to?

It could be that the universe is finite in which case it has a radius. Traveling in a straight line one would very roughly return to the point at which one started. It seems that the Universe would look pretty much the same at every point in the journey.

The CMBR should not exist at a certain point or rather, there should be a point where there is no temperature.

The wavelength could eventually be close to infinity.
 
  • #3
See but that's just it, we are answering infinity with infinity.

For example, when you say that the wavelength could tend to infinity, how can that possibly be true other than in theory? I mean assume that the wavelength keeps getting longer and longer, the frequency will decrease (more distance between peaks), then at some point (infinity), there is no trough or wave because you could not define when the next peak will occur? but what does this say about the amplitude? is it even a wave? the curvy sine wave would just keep going in 1 direction or the other and never turn at any maximum or minimum which doesn't exist? how can this be possible?

Also, I don't think the Universe has infinite matter even if it extends to infinity. This would be because the Universe had a definite temperature at creation (this is a lie, it had a definite temperature, the Planck temperature at Planck Time) and therefore an equivalent definite mass.

Another way of looking at this is knowing that infinite matter and antimatter could not interact. They had to be finite.

I guess I might have phrased it wrong. i should really have asked what the nature of vacuum is.

I guess I would simply ask what happens if a spacecraft (voyager) just keep going out there, does it hit a brick wall (not literally)? I know we have had these questions many times in the past but seriously, some people have suggested that this depends on the geometry of the Universe and that it might be possible to come back where you start. My question then would be is there an energy or certain velocity that would eject you outside the Universe? like imagine if you were moving on the balloon analogy of our Universe? could you ever leave the surface?

These questions seem amateurish but I think I really want to hit at the concept of infinity!

What sort of definite mechanism can create infinity? perhaps a loop like system but what enables it?

Also, want to jump into math theory for a second. Take Pi, we don't know its exact value other than in fraction. Does this mean we never accurately know what the radius, area or volume of a sphere is? (other than in fraction?) I suppose we would know it if the radius was 7 or a multiple in that it would cancel the 7 on the bottom but other than that? I'm trying to get tot he larger picture of what it means that we are unable to get exact definite values for the constants we have like G and h. Would there be any significance to those digits we are dropping in terms of exactly understanding out Universe?

(on a side note, does a photon experience time?)

Lastly, if the Universe was infinite, shouldn't CMBR have radiated to infinity already to give 0 K?

I mean if you have a glass of hot water in an infinite ocean of cold water...or is the CMB itself infinite then? which means infinite photons?
 
  • #4
You should review Cantor's theory on infinities.
 
  • #5
Most problems with infinity arise from the fact that it's frequently confused with 'very big' rather than what it really is.
Infinity simply cannot exist in the same domain as dimensionality - and since we live in a universe with dimensions and dimensionality, infinity cannot exist within it.
So within the universe, it's just a construct of the human mind - and cannot be used for calculations of realworld problems ... only in whole-universe theorisation.
Understanding the origins of the universe will necessarily mean an understanding of the manner in which finity (dimensionality) and infinity sit 'relative' (for want of a better term) to one another.
 
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  • #6
Perchie said:
Infinity simply cannot exist in the same domain as dimensionality - and since we live in a universe with dimensions and dimensionality, infinity cannot exist within it.
Are there not an infinite number of real numbers in the interval [0,1]?
 
  • #7
bapowell said:
Are there not an infinite number of real numbers in the interval [0,1]?
Not in the real world, where there is a limit to the divisibility of matter ... assuming the existence of fundamental particles.
If something conceptual cannot be applied to the physical world, then it's virtual ... a construct of the human mind - it is not of the realm of reality.
 
  • #8
Perchie said:
Not in the real world, where there is a limit to the divisibility of matter ... assuming the existence of fundamental particles.
If something conceptual cannot be applied to the physical world, then it's virtual ... a construct of the human mind - it is not of the realm of reality.
Why can't there be an infinite number of particles in an infinite universe?
 
  • #9
bapowell said:
Why can't there be an infinite number of particles in an infinite universe?
No reason at all.
But there can't be an infinite number in a finite universe.
 
  • #10
Perchie said:
No reason at all.
But there can't be an infinite number in a finite universe.
Sure. Who would dispute this?
 
  • #11
But there can't be an infinite number in a finite universe.

Why not, our visible universe is finite, limited in time, but may be infinite at both extremes.
 
  • #12
bapowell said:
Sure. Who would dispute this?
... ehem.
 
  • #13
petm1 said:
Why not, our visible universe is finite, limited in time, but may be infinite at both extremes.
For the same reason you can't get a quart into a pint pot.
 
  • #14
Since we don't know if the universe is finite or infinite your argument seems mute.
 
  • #15
skydivephil said:
Since we don't know if the universe is finite or infinite your argument seems mute.
My argument was that infinity is not a valid operand in calculations applied to the real world.
(And it's 'moot')
 
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  • #16
Perchie said:
My argument was that infinity is not a valid operand in calculations applied to the real world.
(And it's 'moot')
Unless the universe is infinite in spatial extent.

And I'm curiuos for you to elaborate on your "ehem"...by all means explain how a finite volume can accommodate an infinite number of particles of finite volume.
 
  • #17
It's an emergent result of numeric processes on specific models and theories (Cosmology: Flat and Euclidean Universe) .Invalid, unreal and hard to get by but 'useful and applicable' (fractals, infinite series, imaginary number and so on).

One way of dealing with infinite is to build counter model and hope our observation agrees 'more' with it.
 
  • #18
My teacher told me that parallel lines meet at infinity, however I am pretty sure that they dont, and even if they did it is so far away that it doesn't matter much to me all the way back here. I am not sure if that helps :)
 
  • #19
Tanelorn said:
My teacher told me that parallel lines meet at infinity, but I am pretty sure that they dont, and even if they did it is so far away that it doesn't matter much to me all the way back here. I am not sure if that helps :)
They don't. (In Euclidean space, that is.)
 
  • #20
osxraider said:
See but that's just it, we are answering infinity with infinity.

For example, when you say that the wavelength could tend to infinity, how can that possibly be true other than in theory? I mean assume that the wavelength keeps getting longer and longer, the frequency will decrease (more distance between peaks), then at some point (infinity), there is no trough or wave because you could not define when the next peak will occur? but what does this say about the amplitude? is it even a wave? the curvy sine wave would just keep going in 1 direction or the other and never turn at any maximum or minimum which doesn't exist? how can this be possible?

Also, I don't think the Universe has infinite matter even if it extends to infinity. This would be because the Universe had a definite temperature at creation (this is a lie, it had a definite temperature, the Planck temperature at Planck Time) and therefore an equivalent definite mass.

The wavelength TENDS to infinity, but it never gets there.

If the universe is infinitely large and homogenous, then it has infinite mass and energy. It can still have a definite temperature. Temperature is (very roughly) heat energy divided
by volume. If they are both infinite then one may not divide to get the ratio. But a physicist may measure the temperature and get the ratio that way, so this isn't a problem.
 
  • #21
Tanelorn said:
My teacher told me that parallel lines meet at infinity, however I am pretty sure that they dont, and even if they did it is so far away that it doesn't matter much to me all the way back here. I am not sure if that helps :)

Parallel lines, by definition, never meet. Parallel lines meeting at infinity is correct in one sense, in that, for instance, for a right triangle, as a leg and the hypotenuse approach being parallel, the point of intersection approaches being infinitely far off. This, however, doesn't mean they meet at infinity, saying so would be as correct as saying 1/0=∞.

bapowell said:
Unless the universe is infinite in spatial extent.

Absolutely correct. And I'd like to clarify this to everyone by saying that this doesn't mean that there's a point we can go out to which is an infinite distance away from our starting point, but it means that we can get however far away we want from our starting point.
 
  • #22
Division by zero yields illogical results.
 
  • #23
Precisely, saying parallel lines meet at infinity also yields illogical results.
 
  • #26
bapowell said:
I suppose Whovian should have stipulated that he was referring to Euclidean space with trivial topology.

I suppose you mean standard not trivial topology, and it is not really the topology but the geometry that he means.
 
  • #27
bapowell said:
I suppose Whovian should have stipulated that he was referring to Euclidean space with trivial topology.

True, should've clarified that, I assumed most teachers would be talking about euclidian space.

To martinbn, I was talking about the geometry, but the topology should be quite relevant.
 
  • #28
Well, I see there has been an intense debate.

Well, I'll start my addressing the first replies since my last post.

I haven't reviewed Cantor but does it have to do with claiming 1 infinity is bigger than the other? This would seem like a contradiction and most likely is. Even if there is a work around mathematically, I'm not sure how that would translate into anything physical.

"Are there not an infinite number of real numbers in the interval [0,1]?"

I think this is a cheat. Math allows the creation of all sorts of numbers but they might not have any physical significance. The minimum distance that we could ever move physically is the Planck length. Of course, we could move 0 distance but that would correspond to not moving at all. You can specify a distance that is less than the Planck length but that could never be realized in the real world. Of course you could say the same thing about time and other such things.

As for parallel lines meeting at infinity, this seems like a contradiction. Again, if they ever meet at any point 1.) they are not parallel 2.) the subtle implication is that infinity is a definite point in space where something happens.

As for an infinite Universe having a definite temperature, I don't think this is possible. An infinite Universe can have infinite volume and things like that but I think the temperature would be zero then. The temperature would tend to zero as it is diluted into an infinite volume.

I'm sure I could be wrong but even given my blunt reasoning, what happens if you just keep traveling out into space. Assuming you can beat the rate of expansion and have A LOT of time, you should be able to overtake it? So what happens, do you hit a wall? the Universe's wall/bounds?

or that fact that you are suddenly farther out and technically part of the Universe, then the Universe is bigger now because you're out there?

Which also begs the question, what is the nature of space. Some say that space itself was created in the big bang. But with definite creation and in definite time, the Universe could have not have already become infinity? I know that some will say that the big bang happened everywhere but the Universe essentially came out of a singularity. We know singularities, they are at the centers of black holes. We can mark a definite point in space as a singularity yet the Big Bang singularity was everywhere or is it because we are inside this singularity which then became bigger and so from our perspective, it happened everywhere except that it didn't really happen everywhere but that everywhere was once the same place? correct?

But still, we can imagine an observer from outside this Universe and wonder's about his/her perspective? or can such an observer not even exist because there is nothing to exist in? After all, all these documentaries start of with a tiny little light that explodes into everything.

Can someone shed more light on singularities in the context of this discussion. Saying a little more about their nature mathematically and physically than just saying, point of infinite density and gravity and 0 volume would be helpful.

Also, I'm very well aware of my "amateurish-ness" with my questions and reasoning but I really am trying very hard to wrap my head around this. I understand we don't have all the answers yet but its always comforting to know that other people think about this and so many are trying to figure this out.

Also, one question: There is definitely a mechanism that enables the Universe/universes to form. We can agree on that. My question would then be what enables the mechanism that enables? so you see, we could keep on asking this question. Is there an ultimate? because even if these processes were circular, how would they even begin to exist? what mechanism enables circular mechanisms? if these processes are linear, the they tend to infinity in either direction?

so my question is, should I accept at this point that certain things might just be infinite but because of their infinite nature (that they will always be out of reach), it will never really matter "what's out there at infinity"?

[I'm all over the place but I hope you are able to consolidate all my questions and thoughts]
 
  • #29
I haven't reviewed Cantor but does it have to do with claiming 1 infinity is bigger than the other?

Yes it does. Read it, it is a simple argument. You seem to be interested in such things.

As for an infinite Universe having a definite temperature, I don't think this is possible. An infinite Universe can have infinite volume and things like that but I think the temperature would be zero then. The temperature would tend to zero as it is diluted into an infinite volume.

If the amount of energy were finite then your argument would be correct. But there is no reason to think that. If the Universe is infinite and homogenous, then the amount of energy is infinite.

I'm sure I could be wrong but even given my blunt reasoning, what happens if you just keep traveling out into space. Assuming you can beat the rate of expansion and have A LOT of time, you should be able to overtake it? So what happens, do you hit a wall? the Universe's wall/bounds?

This has got to be in numerous FAQs somewhere, so maybe you should go read that. The basic answer is that space itself is expanding in the same way everywhere. Every part looks more or less like every other part.

I know that some will say that the big bang happened everywhere but the Universe essentially came out of a singularity. We know singularities, they are at the centers of black holes.

Not every singularity is the same. The Big Band was very different from a black hole. There is no relation.

After all, all these documentaries start of with a tiny little light that explodes into everything.

Yep. Well, it's just plain wrong so the first thing is to erase that from one's mind.

Can someone shed more light on singularities in the context of this discussion. Saying a little more about their nature mathematically and physically than just saying, point of infinite density and gravity and 0 volume would be helpful.

In general a singularity is where our math stops making sense. IMO singularity is a more elegant name than "WTF." We have very little idea of what was going on at the very beginning of the Big Bang. It could have been a quite complicated process about which we have no idea whatsoever.

Also, one question: There is definitely a mechanism that enables the Universe/universes to form. We can agree on that. My question would then be what enables the mechanism that enables? so you see, we could keep on asking this question. Is there an ultimate? because even if these processes were circular, how would they even begin to exist? what mechanism enables circular mechanisms? if these processes are linear, the they tend to infinity in either direction?

We dunno. IMO people who speculate about this are wasting their time. It makes more sense to wait until there is some data. Now we have nothing at all.

so my question is, should I accept at this point that certain things might just be infinite but because of their infinite nature (that they will always be out of reach), it will never really matter "what's out there at infinity"?

As far as an infinite universe is concerned, the idea is that every part looks pretty much the same as every other part.
 
  • #30
"In general a singularity is where our math stops making sense. IMO singularity is a more elegant name than "WTF.""
lol, brilliant,that really made me laugh. But now I am coming round to the idea of renaming the singualrity WTF is a good idea.
In all seriosuness there are attemtps to resolve the singualrity. To me the most devleoepd fo these is in loop quanutm cosmology.
You can read about it here:
http://arxiv.org/abs/0812.4703

There is work going to see what thsi means for the polarisation of the CMB . I don't think is a waste of time and we shoudl wait for more data. If they theory makess prediction for the next set fo data (hopefully the B mode polarisation) and it matches that people will be far mroe impressed if the theoy is developed after the data is already out, then some might say it was fitted to meet the data we already know.
 
  • #31
skydivephil said:
... I don't think is a waste of time and we shoudl wait for more data. If they theory makess prediction for the next set fo data (hopefully the B mode polarisation) and it matches that people will be far mroe impressed if the theoy is developed after the data is already out, then some might say it was fitted to meet the data we already know.

Odds are in favor(only way) with B mode due to some good features in such that we can deduced the confusion of radio signals, accuracy of weeping beam strategy and even with circular scan strategy and posses answers to uniformity of CMB, scale invariant of initial conditions and why Ω = 1? (cmb observations fit LCDM standard cosmological model) Which appears to be infinite?

One prediction is that gravity waves of all sizes might be apparent during the primordial universe.

Will the LCMD be consistent still? :tongue2:

I still find some interesting stuff in ekpyrotic prediction (cyclic universe) by Paul Steinhardt and Neil Turok. :biggrin:. Maybe the universe is infinite at all or Not but sure 'looks' that way for now.
 
  • #32
osxraider said:
I think this is a cheat. Math allows the creation of all sorts of numbers but they might not have any physical significance. The minimum distance that we could ever move physically is the Planck length.
You know this? I wasn't aware there was a complete theory of quantum geometry. Do send it my way! ;)
As for an infinite Universe having a definite temperature, I don't think this is possible. An infinite Universe can have infinite volume and things like that but I think the temperature would be zero then. The temperature would tend to zero as it is diluted into an infinite volume.
But the big bang happened everywhere in the universe at once -- even if it is infinite. There should be no trouble in assigning an energy density to the resulting radiation that fills the universe, and questions about establishing thermal equilibrium notwithstanding, assigning a temperature to this radiation. The CMB is 2.7 K, whether or not the universe is infinite.

I'm sure I could be wrong but even given my blunt reasoning, what happens if you just keep traveling out into space. Assuming you can beat the rate of expansion and have A LOT of time, you should be able to overtake it? So what happens, do you hit a wall? the Universe's wall/bounds?
Nobody knows, but it's unlikely that the universe has a boundary (unlikely mostly in an aesthetic sense) A popular conception of a closed universe is a sphere, or more generally, a closed manifold without boundary. The universe could also be infinite (of course, it's important to distinguish between the observable universe, which is of finite volume and has a well-defined boundary, and *the* universe.)

We know singularities, they are at the centers of black holes.
The centers of black holes are examples of singularities -- singularities are a general feature in relativity. A gravitational singularity occurs whenever/wherever the gravitational field (metric) becomes infinite.
We can mark a definite point in space as a singularity yet the Big Bang singularity was everywhere or is it because we are inside this singularity which then became bigger and so from our perspective, it happened everywhere except that it didn't really happen everywhere but that everywhere was once the same place? correct?
The big bang singularity is not something that should be interpreted physically -- it is sign that the theory is broken at that point. Infinite densities and their associated singularities are nonphysical, and so ultimately something must replace the big bang singularity.

After all, all these documentaries start of with a tiny little light that explodes into everything.
Yes, and those producers should all be fired.


Also, one question: There is definitely a mechanism that enables the Universe/universes to form. We can agree on that. My question would then be what enables the mechanism that enables? so you see, we could keep on asking this question. Is there an ultimate? because even if these processes were circular, how would they even begin to exist? what mechanism enables circular mechanisms? if these processes are linear, the they tend to infinity in either direction?
Yes. Until we have a scientific understanding of the physics behind the origin of the universe, we can only resort to philosophy. The infinite regress is a consequence of not knowing the physical bounds of the process.
 
  • #33
Why would the Universe expand at all if it is an infinite Universe? Seems like there would be no reason for any mechanism to operate to expand the Universe if it wasn't expanding it to an amount that was "balanced" so to say. This might sound like a bad question because it might imply purpose and regardless of anything, the Universe has been observed to be expanding but...

Anyway, I guess I am simplifying it to a great extend. For example, heat flows only when there is difference of temperature. What purpose does the expansion fulfill. I mean sure, we can say that if this was slightly different or that was slightly different, we wouldn't be here to observe it but regardless of whether we are here or not, why is the mechanism for expansion operating? if not to fulfill a certain role.

Also, I tried looking into Cantor's infinity theory but couldn't make sense of it. It involves cardinality and powerset (which I have trouble grasping.)

Could someone please shed some light on this? (in a simplistic manner using an appropriate analogy?)

Also, could someone shed some light on the black hole- white hole theory? to me it sounds very appealing that there are other Universes through black holes and what we see as a black hole in out universe is seen as a white hole/big bang in another Universe. There is just one problem. What is the first black hole in this branching universe set (again comes in infinity.) But is this recognized as a plausible theory or is the M-Theory with branes more appealing?

Bapowell:I was able to understand all your responses except for the one about Planck length. Am I not right about that? the problem is we don't know what replaces the laws of physics below Planck length (or whether any law even exists that governs such a distance scale) because as far as I have gathered from sources, it should be the minimum physical distance (given the the physics we know today.) In that sense, it is incomplete but correct me if I'm wrong.
 
  • #34
osxraider said:
Bapowell:I was able to understand all your responses except for the one about Planck length. Am I not right about that? the problem is we don't know what replaces the laws of physics below Planck length (or whether any law even exists that governs such a distance scale) because as far as I have gathered from sources, it should be the minimum physical distance (given the the physics we know today.) In that sense, it is incomplete but correct me if I'm wrong.
No, you are absolutely correct -- we don't know what happens to geometry on scales beyond the Planck length. You seemed to be suggesting a discrete spacetime in response to my earlier post regarding the fact that there are an infinite number of reals in the interval [0,1]. Now, I don't necessarily disagree with this view of a discrete spacetime, but we simply don't know yet what the nature of spacetime is at these scales: it could be discrete, or it coule be something else entirely.
 
  • #35
osxraider said:
Why would the Universe expand at all if it is an infinite Universe?
Expansion is a local property. A loose analogy you might be able to visualize is to imagine standing on an immense sheet of rubber, to which you've attached a bunch of stickers. If the sheet of rubber started to distort so as to make your stickers move apart, you could say that the sheet of rubber is expanding here where you're standing, even though you know nothing about what is happening everywhere else.

What purpose does the expansion fulfill.
The word "purpose" has connotations irrelevant to physical law...

Also, I tried looking into Cantor's infinity theory but couldn't make sense of it. It involves cardinality and powerset (which I have trouble grasping.)
The notion of cardinality studied in set theory is mostly unrelated to the number [itex]+\infty[/itex] that appears in continuous mathematics.


as far as I have gathered from sources, it should be the minimum physical distance (given the the physics we know today.)
To the best of my knowledge, this idea is still speculative -- there is not yet anything to back up the idea that there is a minimum distance, simply evidence suggesting we look for new theories having this property.
 

1. What is infinity and why is it important to explore theories about it?

Infinity is a concept that represents something that has no limit or end. It is important to explore theories about infinity because it allows us to better understand the universe and the fundamental nature of reality.

2. How do scientists approach the concept of infinity?

Scientists approach the concept of infinity using mathematical and philosophical theories. They also use empirical evidence and observations from the natural world to inform their understanding of infinity.

3. Can we ever truly understand or grasp the concept of infinity?

It is debatable whether we can ever fully understand or grasp the concept of infinity. Some argue that our finite minds are not capable of comprehending something that has no limits. However, through continued exploration and research, we can gain a deeper understanding of infinity.

4. How does the concept of infinity relate to the concept of time?

Many theories about infinity suggest that time may be infinite, meaning it has no beginning or end. This idea challenges our traditional understanding of time as a linear and finite concept. Exploring theories of infinity can help us better understand the nature of time and its relationship to the universe.

5. Are there any practical applications for theories of infinity?

While theories of infinity may seem abstract and theoretical, they have practical applications in fields such as mathematics, physics, and computer science. Understanding infinity can also lead to advancements in technology and our understanding of the universe.

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