# Is the Universe Infinite? Or is only God Infinite?



## LadyCalvinist

Hello,

I recently heard someone say that the Universe cannot be infinite because only God is truly infinite. Is this true?


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## Miss Marple

I always thought, draw a line around the universe, well, something's on the other side of the line. So it's infinite, like numbers. You can always add "one."

But I may not be thinking it through well enough, I don't know.


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## Loopie

I suppose a distinction also should be made between infinite and eternal. Certainly the universe is not eternal, and only God himself is eternal. As for the actual 'size' of the universe, that I cannot speak on.


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## Romans922

The universe is not infinite. It is created and thus cannot be infinite.


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## Mushroom

Since space and time are equivalencies, wouldn't that make infinite space and eternal time equivalencies? And if so, since only the triune God is eternal, wouldn't that mean that only God could be infinite?

If that is so, then no, the physical universe is not infinite in space.


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## Skyler

Romans922 said:


> The universe is not infinite. It is created and thus cannot be infinite.



Our lifespan is infinite, and yet we are created.

Since the heavens and earth will exist forever, in their recreated form, in that sense we can say that the universe is infinite into the future. (Whether that applies to the current universe or whether there will be a disconnect of destruction and recreation is a valid question.)

Whether the universe is infinite in space is another question. For philosophical reasons, I do not believe it is. Hilbert's Hotel paradox, among others, seems to obviate the possibility of an actually infinite set (as opposed to the "potentially infinite" of the created but undying universe).


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## littlepeople

Modern science indicates that the universe is not infinite. It's a peculiar proof of the existence of God that we have an idea of "infinite" that is fixed in our minds, yet outside of God, it doesn't exist in the real world. This is true of the infinitely large, and the infinitely small. Space comes in defined packets or quanta - so there is no such thing as the infinitely small point; you do reach a point at which you cannot subdivide any smaller.


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## ChristianTrader

Loopie said:


> I suppose a distinction also should be made between infinite and eternal. Certainly the universe is not eternal, and only God himself is eternal. As for the actual 'size' of the universe, that I cannot speak on.



I think infinite and eternal imply each other. If you are one then you are the other or if you are not one then you cannot be the other.

CT


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## SolaScriptura

Skyler said:


> Romans922 said:
> 
> 
> 
> The universe is not infinite. It is created and thus cannot be infinite.
> 
> 
> 
> 
> Our lifespan is infinite, and yet we are created.
Click to expand...


Actually, our lifespan is not infinite. For something to be infinite it must be endless in every direction. But our lifespan is only endless in one direction. In geometric terms, a line is infinite because it goes, endlessly, in both directions. Our lives are more appropriately compared to a ray - which has a definite starting point, and goes endlessly in one direction proceeding from that point. 

Concerning the universe, I've always considered that the universe may be so massive that from our perspective it may seem infinitely large, yet our Lord is so infinitely greater that he holds all of the created order in his hand.


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## Paul1976

Science has shown in a number of ways that the universe cannot be infinite. One of the simpler ones is the fact that the night sky is black. If you work out how light spreads out from galaxies (things get dimmer as they get farther away), and how light would build up from more and more galaxies at progressively farther distances, the sky should be white in an infinite universe. Not just white, but blindingly, searingly white from an infinite amount of light. Thankfully, this is not the case, as is possible only for a finite universe. Anyone wanting more details could find them I'm sure - I remember seeing the math and there is nothing beyond high school algebra to convince yourself of this.

A finite universe brings up an interesting quandry. What's at the end of the universe? If the universe ended at, say, a brick wall, we would wonder what was on the other side of it. It doesn't work that way. While I cannot prove this as easily with words, hopefully this picture will give you an idea how we can have a finite universe without any brick walls with nothing on the other side of them. The four dimensional nature of space time means space can be bent. This was predicted by Einstein with his general theory of relativlity. The curvature of space not only makes sense if you take enough university physics classes on the subject, but it's been verified by a number of experiments for nearly 100 years now. 

Here is a picture that will help. Planet Earth is a 3D object of finite size. We live on the surface of it, where it appears flat and two-dimensional. Yet, we can go as far as we like in any direction, and never hit any brick walls (minus the ones we build, of course). We might eventually go around and end up at the same point we started from, but there is no end. Moving around in 3D in a 4D universe yields the same results. We can go as far as we like, but the curvature of space restricts us to a finite volume of space. There are more formal and convincing explanations (not all of which I understand!), but hopefully this is a good picture.


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## KMK

Has no one read, "Horton Hears A Who"?


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## Paul1976

KMK said:


> Has no one read, "Horton Hears A Who"?



No. Who is it by?


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## Skyler

SolaScriptura said:


> Skyler said:
> 
> 
> 
> 
> 
> Romans922 said:
> 
> 
> 
> The universe is not infinite. It is created and thus cannot be infinite.
> 
> 
> 
> 
> Our lifespan is infinite, and yet we are created.
> 
> Click to expand...
> 
> 
> Actually, our lifespan is not infinite. For something to be infinite it must be endless in every direction. But our lifespan is only endless in one direction. In geometric terms, a line is infinite because it goes, endlessly, in both directions. Our lives are more appropriately compared to a ray - which has a definite starting point, and goes endlessly in one direction proceeding from that point.
Click to expand...


To pick an abstract example, that would mean that the set of positive integers is not infinite (because it is endless in only one direction, but has an end at 0). But the set of positive and negative integers _would_ be infinite, because it is endless in both directions. Unless I'm misremembering my math both of the above sets are technically "infinite".

The difference between the two is that, for a ray, any point on the ray is a finite distance from the beginning - yet the ray still continues on indefinitely. This is analogous to our lifespan within the context of time - at any given moment (point) in time, we have existed for a finite amount of time, yet taken as a whole our lifespan reaches on infinitely into the future.


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## Skyler

Paul1976 said:


> KMK said:
> 
> 
> 
> Has no one read, "Horton Hears A Who"?
> 
> 
> 
> 
> No. Who is it by?
Click to expand...


Dr. Seuss. It's a good read.


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## ZackF

Thomas Aquinas made the helpful distinction between the eternal and aveternal. God (eternal) creates angels (aveternal), men (aveternal) and places/relationships like Hell (aveternal). He also creates completely finite things like worms and cigarettes.


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## Steve Paynter

Skyler said:


> To pick an abstract example, that would mean that the set of positive integers is not infinite (because it is endless in only one direction, but has an end at 0). But the set of positive and negative integers _would_ be infinite, because it is endless in both directions. Unless I'm misremembering my math both of the above sets are technically "infinite".



You are not misremembering your maths. A set is defined to be infinite if it can be placed in one-to-one correspondence with a proper subset of itself. Hence, to continue your example, the set of natural numbers is infinite because it can be placed in one-to-one correspondence with the set of even natural numbers. E.g. 

0 - 1 - 2 - 3 - 4 ....
.|...|....|...|....| 
0 - 2 - 4 - 6 - 8 ....

(Furthermore, the rule relating them can be expressed in a finite way - no axiom of choice is needed.) Hence both the set of natural numbers is infinite. Furthermore, so is the set of even natural numbers. In fact the fact that the two sets can be placed in one-to-one correspondence with each other shows that
they are the same size .... the first infinity, omega. 

(Most) Mathematicians, of course, deal with completed infinities, and with power-sets (sets of all the subsets of a set) of any set, including infinite ones. This leads to transfinite numbers ... sets bigger than infinite sets, and hence to all the wonder of transfinite numbers.

If Cantor's diagonalization argument is accepted, there are more real numbers (between 0 and 1, say) than there are integers.

Anyway, your point remains ... something doesn't have to be infinite in more than one way to be infinite. In fact, mathematicians do not accept that there are more integers than naturals, as again it is a simple matter to define a rule which places them in one-to-one correspondence.

0 -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 ....
.| .. | .... | .. | .... | .. | .... | .. |
0 .. 1 .. -1 .. 2 .. -2 .. 3 .. -3 .. 4 ....


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## Steve Paynter

I have toyed with the idea that the universe cannot be infinite because in an infinite universe everything happens somewhere, and this would be incompatible with God's righteousness. However, I have come to reject it, because it does not follow that in an infinite universe, everything happens somewhere. The infinite universe may simply repeat itself ... over and over and over ... again.

I personally am unclear whether being infinite in space is a uncommunicable attribute of God. It may be, but I can't see the argument why it must be. However, I agree that the scientific evidence seems to be that we do not in fact live in an infinite universe.


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## Rangerus

it is infinity and beyond


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## a mere housewife

'. . . who stretches out the heavens like a curtain,
and spreads them like a tent to dwell in . . . '
Isaiah 40:22


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## Claudiu

Ah, eternity and infinity. Concepts we don't much understand!


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## Steve Paynter

Paul1976 said:


> Science has shown in a number of ways that the universe cannot be infinite. One of the simpler ones is the fact that the night sky is black. If you work out how light spreads out from galaxies (things get dimmer as they get farther away), and how light would build up from more and more galaxies at progressively farther distances, the sky should be white in an infinite universe. Not just white, but blindingly, searingly white from an infinite amount of light. Thankfully, this is not the case, as is possible only for a finite universe.



Does this argument only work if the infinite universe has existed for an infinite amount of time? If it had a beginning (as we believe that it does), then there will be parts of the universe that contains light sources (suns) which have not yet reached us. Maybe there are only a finite number of suns in the part of the universe that has had time to impact our night sky. Of course, for science, this would raise the problem of how we would know it was there.


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## a mere housewife

I like to think camels are infinite. In my own mind, numbers are symbols for trains of camels. And the negative numbers are symbols for camel trains going the other way. So if the camels start at a single point and go in both directions forever, they could fill all of space. And if they reach a brick wall they could jump off. And even if there is only really a single small, little camel, and it's only that the rope which might tie it to another imaginary camel could be tied endlessly in repetitive motions forever, I can still cross my eyes and see another camel, and pretend they are both joined by friends, and so on, until they are all jumping off of brick walls at the end of a donut. . . 

I'm not math minded, but thanks to camels, I do have a conceptual framework for some of these things.


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## Skyler

Steve Paynter said:


> Paul1976 said:
> 
> 
> 
> Science has shown in a number of ways that the universe cannot be infinite. One of the simpler ones is the fact that the night sky is black. If you work out how light spreads out from galaxies (things get dimmer as they get farther away), and how light would build up from more and more galaxies at progressively farther distances, the sky should be white in an infinite universe. Not just white, but blindingly, searingly white from an infinite amount of light. Thankfully, this is not the case, as is possible only for a finite universe.
> 
> 
> 
> 
> Does this argument only work if the infinite universe has existed for an infinite amount of time? If it had a beginning (as we believe that it does), then there will be parts of the universe that contains light sources (suns) which have not yet reached us. Maybe there are only a finite number of suns in the part of the universe that has had time to impact our night sky. Of course, for science, this would raise the problem of how we would know it was there.
Click to expand...


That, and then there's the fact (as mentioned) that light gets dimmer as it gets further away. Even if there is an infinite number of galaxies, if they are distributed evenly, the light from them would have an average finite peak because each of those galaxies emits a finite number of photons. If you assume that photons from all galaxies would eventually reach ours, you could still have infinite light - but what's to keep photons from colliding with galaxies, space dust, etc. in between? For any given direction, there will be some object at some finite distance from us that is sufficient to block or divert light particles from further in that direction. Therefore, only a finite number of photons can reach us at any given time.

Am I off here?


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## SRoper

Skyler said:


> Steve Paynter said:
> 
> 
> 
> 
> 
> Paul1976 said:
> 
> 
> 
> Science has shown in a number of ways that the universe cannot be infinite. One of the simpler ones is the fact that the night sky is black. If you work out how light spreads out from galaxies (things get dimmer as they get farther away), and how light would build up from more and more galaxies at progressively farther distances, the sky should be white in an infinite universe. Not just white, but blindingly, searingly white from an infinite amount of light. Thankfully, this is not the case, as is possible only for a finite universe.
> 
> 
> 
> 
> Does this argument only work if the infinite universe has existed for an infinite amount of time? If it had a beginning (as we believe that it does), then there will be parts of the universe that contains light sources (suns) which have not yet reached us. Maybe there are only a finite number of suns in the part of the universe that has had time to impact our night sky. Of course, for science, this would raise the problem of how we would know it was there.
> 
> Click to expand...
> 
> 
> That, and then there's the fact (as mentioned) that light gets dimmer as it gets further away. Even if there is an infinite number of galaxies, if they are distributed evenly, the light from them would have an average finite peak because each of those galaxies emits a finite number of photons. If you assume that photons from all galaxies would eventually reach ours, you could still have infinite light - but what's to keep photons from colliding with galaxies, space dust, etc. in between? For any given direction, there will be some object at some finite distance from us that is sufficient to block or divert light particles from further in that direction. Therefore, only a finite number of photons can reach us at any given time.
> 
> Am I off here?
Click to expand...


Steve,
If the universe was infinite in extent but had a starting point in time we would expect the radiation (light) reaching us to increase with each year.

Jonathan,
You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.


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## Steve Paynter

SRoper said:


> Steve,
> If the universe was infinite in extent but had a starting point in time we would expect the radiation (light) reaching us to increase with each year.



This is an interesting observation. Does the argument also apply to universes which are finite but simply much bigger than what we have seen so far ... because of perhaps, inflation during the early moments?

(For those who don't know, some scientists have hypothesised that for a brief moment of time soon after the big bang, the universe underwent a period of "inflation", when it grew much faster than the speed of light. They suggest that not only is this theoretically possible, but that it would explain the "flat" nature of space - suggesting that it is much bigger than we have yet seen.)

I wonder if this argument fails because it also makes assumptions about the density of light sources in a possible infinite universe. In other words, perhaps this is happening, but we haven't been taking careful measure of the light reaching us for long enough for it to be noticeable, given the relatively low density of the universe.


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## earl40

Are angels and demons in our universe? If so can we say they are supernatural? I think of them as being in time like us thus they are supernatural beings in our universe from our preception but natural beings in our universe from the perspective of God.

Thoughts?


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## Skyler

earl40 said:


> Are angels and demons in our universe? If so can we say they are supernatural? I think of them as being in time like us thus they are supernatural beings in our universe from our preception but natural being in our universe from the perspective of God.
> 
> Thoughts?



Angels are described as moving between heaven and earth, from God's throne to man and back again. I think it's safe to say that God's "cosmos" extends beyond our universe.


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## earl40

Skyler said:


> Angels are described as moving between heaven and earth, from God's throne to man and back again. I think it's safe to say that God's "cosmos" extends beyond our universe.



I would extend a few more " "....I think it's safe to say that God's "cosmos" "extends" "beyond" our universe.


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## Skyler

earl40 said:


> Skyler said:
> 
> 
> 
> Angels are described as moving between heaven and earth, from God's throne to man and back again. I think it's safe to say that God's "cosmos" extends beyond our universe.
> 
> 
> 
> 
> I would extend a few more " "....I think it's safe to say that God's "cosmos" "extends" "beyond" our universe.
Click to expand...


I was speaking conceptually, not spatially... but yes.


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## earl40

Skyler said:


> earl40 said:
> 
> 
> 
> 
> 
> Skyler said:
> 
> 
> 
> Angels are described as moving between heaven and earth, from God's throne to man and back again. I think it's safe to say that God's "cosmos" extends beyond our universe.
> 
> 
> 
> 
> I would extend a few more " "....I think it's safe to say that God's "cosmos" "extends" "beyond" our universe.
> 
> Click to expand...
> 
> 
> 
> 
> I was speaking conceptually, not spatially... but yes.
Click to expand...


Thus the universe has limits, in that only God alone can or be outside of time and space. This is why the incarnation was not only necessary but glorious in that Jesus chose to connect with us in time and space.


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## Skyler

SRoper said:


> Jonathan,
> You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.



This is true, but because the universe is composed of discrete units, and radiation sources are not mathematical points, "every point in the sky" still constitutes a finite set of radiation sources (albeit a large one).

For a simple analogy, consider a pixellated circle. From the center of the circle, you can draw a ray in any direction, but it will always intersect with one of a finite number of pixels.


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## SRoper

Steve Paynter said:


> SRoper said:
> 
> 
> 
> Steve,
> If the universe was infinite in extent but had a starting point in time we would expect the radiation (light) reaching us to increase with each year.
> 
> 
> 
> 
> This is an interesting observation. Does the argument also apply to universes which are finite but simply much bigger than what we have seen so far ... because of perhaps, inflation during the early moments?
> 
> (For those who don't know, some scientists have hypothesised that for a brief moment of time soon after the big bang, the universe underwent a period of "inflation", when it grew much faster than the speed of light. They suggest that not only is this theoretically possible, but that it would explain the "flat" nature of space - suggesting that it is much bigger than we have yet seen.)
> 
> I wonder if this argument fails because it also makes assumptions about the density of light sources in a possible infinite universe. In other words, perhaps this is happening, but we haven't been taking careful measure of the light reaching us for long enough for it to be noticeable, given the relatively low density of the universe.
Click to expand...


I suppose its not so much an argument but, as you said, an observation as to what would necessarily happen. The scale of such an increase is certainly unmeasureable over the timescales we've been making observations. I believe the current understanding in cosmology is that the universe is expanding at an increasing rate such that the extent of the observable universe continues to be less.



Skyler said:


> SRoper said:
> 
> 
> 
> Jonathan,
> You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.
> 
> 
> 
> 
> This is true, but because the universe is composed of discrete units, and radiation sources are not mathematical points, "every point in the sky" still constitutes a finite set of radiation sources (albeit a large one).
> 
> For a simple analogy, consider a pixellated circle. From the center of the circle, you can draw a ray in any direction, but it will always intersect with one of a finite number of pixels.
Click to expand...


I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment? I'm genuinely asking the question because I'm a little hazy on my math. Intuitively I want to say yes because the alternative is that you never reach some point P which would call into the question whether the probability density was truly uniform. I don't know. Weird stuff happens with infinity. I can say with confidence that the sky will appear to be uniformly white at any arbitrary resolution. To use my analog, there exists no interval [P1 P2] where 0 <= P1 < P2 <= 1 where you would not find a point that is in the infinite series of random points.


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## Afterthought

SRoper said:


> I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment?


Seems to me the picking forms a countable set, so no.


Is infinity an incommunicable attribute of God? Perhaps the "infinite" spatial extent is different from God's infinity?


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## SRoper

Afterthought said:


> SRoper said:
> 
> 
> 
> I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment?
> 
> 
> 
> Seems to me the picking forms a countable set, so no.
Click to expand...


Ah, of course you are right, Raymond.


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## Skyler

SRoper said:


> I'm not sure I follow, but it seems to me the situation is analogous to randomly picking a real number between 0 and 1 an infinite number of times. Would you reach every point on the segment? I'm genuinely asking the question because I'm a little hazy on my math.



Mathematically yes; physically, the analogy would only apply if you could only pick numbers in increments, of, say, 0.001 - because there's a limit decreed by the minimum size of the radiation source.


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## hammondjones

Matter/energy may be discrete, but whether or not space-time is discrete is an open question, as far as I know. Even if there is a finite amount of matter in the universe, I don't think that it necessarily follows that the universe itself is finite. Perhaps, though, I am making an unwarranted distinction between the universe and the matter contained in it.


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## SRoper

It has nothing to do with the minimum size of the radiation source, rather it is the position of the radiation source in the sky relative to the observer (elevation and azimuth). As long as there is a nonzero chance of a radiation source in any given direction, there would be a source at every point in the sky resolved to any arbitrary resolution.


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## Afterthought

Afterthought said:


> Is infinity an incommunicable attribute of God? Perhaps the "infinite" spatial extent is different from God's infinity?


I checked a few sources and yes, infinity is considered an incommunicable attribute. So now the question is: does this infinity differ from what we mean when we say the universe is infinite? Perhaps the difference is that God's infinity of being means that all of Him is everywhere, whereas for the infinity of space, the space just goes on and on, rather than all the space being everywhere?


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## Skyler

SRoper said:


> It has nothing to do with the minimum size of the radiation source, rather it is the position of the radiation source in the sky relative to the observer (elevation and azimuth). As long as there is a nonzero chance of a radiation source in any given direction, there would be a source at every point in the sky resolved to any arbitrary resolution.



Yes, but many of those infinite points in the sky would resolve to the same radiation source. Like the pixellated circle, you can draw rays in finer and finer increments, but they would still hit one of a finite number of pixels.

In other words, it's not the number of points in the sky; it's the number of unique radiation sources.


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## The Conductor

It is technically possible to be infinite without repeating oneself or doing everything.
Certain transcendental numbers, for example, contain only ones and zeroes. If one were to convert this into words via some arbitrary number-to-letter conversion, many, if not most words would not appear.



That being said, I don't believe that the universe is infinite, but it would only excite me if I found out it was. The sheer size of the universe compared to the size of the inhabited universe says a lot about God's sovereignty.

Job38:25-27 ESV
“Who has cleft a channel for the torrents of rain
and a way for the thunderbolt,
to bring rain on a land where no man is,
on the desert in which there is no man,
to satisfy the waste and desolate land,
and to make the ground sprout with grass?


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## tommyb

If the universe was infinite how could it be expanding?


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## Brian Bosse

Hello Everyone,

This thread could easily be in the philosophy section. When we speak of 'eternality' and 'infinity', what do we mean? 



Steve said:


> A set is defined to be infinite if it can be placed in one-to-one correspondence with a proper subset of itself.



When Steve speaks of the infinite in terms of the size of a set (its cardinality), he is using 'infinite' as a technical term. In this case, the context is some formal mathematical system - some set theory. As such, this definition is nothing more than a mathematical construct, and may or may not have anything to do with reality. To that end, when the Bible speaks of God being infinite, it would be a mistake to import this or some other meta-mathematical definition into the term. (*Note:* I do not think Steve was doing this. I think he simply was responding to someone else's question about how some mathematicians (not all) use the term 'infinity'.) 

So, what does the Bible mean when it speaks of God's eternality? I think it is safe to say it has nothing to do with Cantor's paradise. 

Sincerely,

Brian


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