You missed the most important premise.

0. Assume your own idiosyncratic definition of 'infinite', with which virtually no-one here seems to agree.

Once we add that, then brilliant... Perfectly valid argument, well done.

I am in this case using the standard definition of infinity: 'something larger than anything else possible'. If it grows it implies it was not larger than anything else possible to start with.

So space must be finite.

That's not the standard definition of infinity and you've had as much explained to you a hundred times.

You've presented your argument about what you think infinity means, most ultimately disagreed. Just have the dignity to accept that instead of keep starting threads which basically hang on exactly the same disputed definition.

The standard definition is:

a number greater than any assignable quantity or countable number

If there exists a number X+1, then X cannot be infinite... so by the standard definition of infinity, my argument holds.

It is accepted by virtually every mathematician that there are an infinite number of negative integers, there are also an infinite number number of positive integers. The number of integers is greater than the number of negative integers (by the number of positive integers), despite all of these being an infinite number.

That is the standard definition of infinity and by it, some infinities are contained within others.

That is the standard definition of infinity and by it, some infinities are contained within others. — Isaac

The size of the universe is either infinite or not infinite. If it can grow, it is by definition not infinite. Only finite sized things can grow.

The DICTIONARY mathematical definition of infinity:

a number greater than any assignable quantity or countable number

There clearly only one such possible number - the existence of such a number by definition rules out any other infinite numbers. There is only one infinity.

Cosmologists/astronomers observe that the light coming from distant galaxies is redshifted. They assume that this redshift is due to these galaxies receding from us. They observe that on average the more distant the galaxy the higher the redshift, so they conclude that the more distant the galaxy the faster it recedes from us. They assume that we do not have a special place in the universe, and so that other galaxies would make a similar observation. They conclude that all galaxies are moving away from each other, at a rate proportional to the distance between them. At that point there is no mention of any "space" expanding, it's just galaxies moving away from each other.

One way to view it is to say that galaxies are staying still while there is some underlying space expanding, but no entity called "space" has ever been observed expanding or stretching, when we say space expands we're saying nothing more than galaxies move away from each other at a rate proportional to the distance between them, which doesn't require an expanding space to describe.

The universe could have been arbitrarily large at the time of the big bang, and could be arbitrarily large today.

Saying the universe is infinite is just fantasy talk, in the sense that's not something that could be deduced from observation. Also the concept of infinity is not something that can be directly grasped, we can conceive of something going on forever, but we can't conceive of the entirety of that thing, so we can't conceive of that entire thing growing bigger. But mathematicians have no problem imagining something that goes on forever inside something that goes on forever, like there being an infinity of real numbers between two natural numbers and there being an infinity of natural numbers, but it's just mind games really. At the end of the day, saying the universe is infinite is the same as saying in some imaginary world pigs can fly, sure we can imagine it but how is it relevant to anything in our lives besides it being some mind game?

One way to view it is to say that galaxies are staying still while there is some underlying space expanding, but no entity called "space" has ever been observed expanding or stretching, when we say space expands we're saying nothing more than galaxies move away from each other at a rate proportional to the distance between them, which doesn't require an expanding space to describe. — leo

But the metric is expanding. So we can equate the metric to space without having to resort to a believe in spacetime. And if the metric is expanding, the metric, IE space, cannot be infinite.

There clearly only one such possible number — Devans99

As I said. The entire mathematical community disagrees with you here. Rather than just make another post about it in a slightly different way, why not try to understand why they've reached that conclusion. Accept that others see things differently, you might learn something.

I've spent years studying infinity and my conclusion is that the mathematical community have it wrong.

Its a belief called Finitism:

https://en.wikipedia.org/wiki/Finitism

Used to be more popular than it is nowadays but there are still a few proponents (Max Tegmark, William Craig Lane) for it around.

You should have respect for and consider other peoples viewpoints; not dismiss them blindly.

You should realise it is a fact that not everything you were taught in school is correct... learn to be more skeptical and keep an open mind to new ideas.

If all you people would just add the words "what we humans consider to be"....to "space" "time" "the universe" "infinity"...and all that lot...

...perhaps the confusion would stop...and the definitive statements like "Space Is Expanding So It Can’t Be Infinite?"...would also stop.

Please, folks, stop thinking that humans are the ultimate thinking machines. Stop supposing that OUR concepts of reality...ARE the REALITY.

There is nothing wrong with a totally blind guess that "infinity " or "eternally" do not exist. But all it will ever be IS A BLIND GUESS.

What we humans consider the universe may be expanding...but "what we humans consider the universe" may be but nothing within an INFINITE universe.

What we humans consider the universe may be expanding...but "what we humans consider the universe" may be but nothing within an INFINITE universe. — Frank Apisa

Good point. If our universe is expanding and our universe is contained in the larger universe, that means the larger universe must be expanding too hence it can't be infinite either.

— Devans99

Devans99
1.1k
↪Isaac
I've spent years studying infinity and my conclusion is that the mathematical community have it wrong.

Its a belief called Finitism:

https://en.wikipedia.org/wiki/Finitism

Used to be more popular than it is nowadays but there are still a few proponents (Max Tegmark, William Craig Lane) for it around.

You should have respect for and consider other peoples viewpoints; not dismiss them blindly.

You should realise it is a fact that not everything you we — Devans99

If anything...it is a BLIND GUESS called Finitism...which you are disguising by calling it a "belief."

It may be correct...and it may be incorrect.

No way to know right now.

That's the way things go with blind guesses about something as unfathomable as the REALITY.

What we humans consider the universe may be expanding...but "what we humans consider the universe" may be but nothing within an INFINITE universe. — Frank Apisa


Good point. If our universe is expanding and our universe is contained in the larger universe, that means the larger universe must be expanding too hence it can't be infinite either. — Devans99

BUT...the REALITY MAY be that all there is...is infinity.

There may be no expanding...just the illusion of expanding.

Sorta like the illusion of the sun going across the sky.

There may be no expanding...just the illusion of expanding — Frank Apisa

What then is your explanation for the redshift of distant galaxies?

But the metric is expanding. So we can equate the metric to space without having to resort to a believe in spacetime. And if the metric is expanding, the metric, IE space, cannot be infinite. — Devans99

Well you can imagine a finite part of the universe and visualize the metric expanding in that part, and imagine that the same goes on in every part of an universe that goes on forever.

Like you can imagine a finite part of the natural numbers (say {1; 2}) and visualize adding real numbers in that part (so it becomes say {1; 1.01; 1.001; 1.0001; 1.00001; ...; 2}), and imagine that the same goes on in all other parts of the natural numbers ({2; 3}, {3; 4}, {4; 5}, ...) that go on forever.

You just can't imagine an infinite universe as a whole doing that, like you can't imagine all the natural numbers at once doing that, you can just imagine the process. Then some might say "our mind is not able to grasp it all at once but that's only a limit of our mind", while others might say "something that cannot be conceived as a whole doesn't exist or is impossible".

you made classic error. Space can ether be the area or the matter. You have use the word space without defining wich one. You argument is true when applied to matter because it is the matter what we mean when we say it is expanding, and I believe matter cannot be infinite. However when applied to the area no longer applys.

Well you can imagine a finite part of the universe and visualize the metric expanding in that part, and imagine that the same goes on in every part of an universe that goes on forever. — leo

If it goes on forever, there is no room for any expansion; there is nowhere to expand to.

Then some might say "our mind is not able to grasp it all at once but that's only a limit of our mind", while others might say "something that cannot be conceived as a whole doesn't exist or is impossible". — leo

I'm of the 2nd believe. That head spinning feeling when we think of infinity is our minds choking on a very illogical concept I think.

However when applied to the area no longer applys. — hachit

Why so? It applies to the metric - that can't be both expanding and infinite at the same times so it applies to space/'the area'?

Devans99
1.1k

There may be no expanding...just the illusion of expanding — Frank Apisa


What then is your explanation for the redshift of distant galaxies? — Devans99

I can make some guesses about what MAY BE the possible explanation:

It may be part of the illusion.

It may be a part of what we humans do not know about physics.

hachit
145
↪Devans99
you made classic error. Space can ether be the area or the matter. You have use the word space without defining wich one. You argument is true when applied to matter because it is the matter what we mean when we say it is expanding, and I believe matter cannot be infinite. However when applied to the area no longer applys. — hachit

There is that term again.

YOU BLINDLY GUESS THAT MATTER CANNOT BE INFINITE.

Aside: There is a decent chance that "matter" is infinite. Science at the moment is saying that matter breaks down into smaller and smaller constituent parts...until at the quantum level...it is suggested that there is nothing but energy...not actual particles of what we humans would call matter.

Well you can imagine a finite part of the universe and visualize the metric expanding in that part, and imagine that the same goes on in every part of an universe that goes on forever. — leo


If it goes on forever, there is no room for any expansion; there is nowhere to expand to.

Then some might say "our mind is not able to grasp it all at once but that's only a limit of our mind", while others might say "something that cannot be conceived as a whole doesn't exist or is impossible". — leo


I'm of the 2nd believe. That head spinning feeling when we think of infinity is our minds choking on a very illogical concept I think. — Devans99

'Nuff said?

Another blind guess being called a "belief."

because area cannot expand. The meter is always a meter it will never get longer. However the problem you are making is not your idea

can't be both expanding and infinite

It is that you say space is expanding, not defining what space your talking about and using both when it works to your advantage.

YOU BLINDLY GUESS THAT MATTER CANNOT BE INFINITE.

When I say it believe I'm saying is have a resoning, but there is always room for doubt.
The reason I believe there isn't an infinite about of matter is because of the propertys of infinite things.

And yes I know about the quantum level.

The astronomers are telling that area is expanding. They liken the expansion of the universe to the expansion of a ballon with dots on it to represent the galaxies.

I've spent years studying infinity and my conclusion is that the mathematical community have it wrong. — Devans99

Yes. I think we've all gathered that. Repeating it doesn't seem to be helping.

If it goes on forever, there is no room for any expansion; there is nowhere to expand to. — Devans99

I'm of the 2nd believe. That head spinning feeling when we think of infinity is our minds choking on a very illogical concept I think. — Devans99

Yes we can't imagine it, we can just imagine the process. Honestly I think those who try to apply the concept of infinity to the universe just do it on aesthetic grounds, they see beauty in the idea of something that goes on forever rather than something with borders. But they couldn't make any objective observation that would prove the universe goes on forever.

maby I should make what I mean by area more clear.

Area, in this context, is all the room matter can be. Astronomers cannot be saying what I call area is expanding or we would know of the answer to this already.

Galaxies are moving apart from each other at greater than the speed of light. That is only possible if space/area is expanding.

no Galaxies are made (ultimately) of matter. The distance between two entity composed of matter is expanding, but that doesn't mean there is any more places for them to take up.

Wittgenstein had a nice solution to stop bothering about these kinds of problems, basically do we ever observe infinite things? No we only observe finite things, and our concept of expansion stems from our observations of finite things that expand, so it is meaningless to apply a concept that applies to finite things to something that is not finite.

But even if you got cosmologists to stop talking about an infinite space that expands, that wouldn't change much in the grand scheme of things.