I am aware that you can classify infinite sets via cardinal numbers. However calling them numbers seems to me a bit of a stretch.
Like I would maybe say that calling the matrix multiplication "multiplication" seems a bit dubious.
It is obviously clear why see similarity between common multiplication, scalar multiplication, matrix multiplication ect. it is also obvious that those concepts are useful.

I think this illustrates that despite similarity in concept and name cardinal numbers and common numbers are different things that one should not confuse. Cardinal numbers get used to quantify infinite sets however if you question infinity it seems problematic that you try to use a concept that is predicated on the existence of multiple infinities to refer to infinity as a number. This somehow negates your own stance, since cardinal numbers don't negate infinity. It's precisely the opposite they acknowledge infinities and try to form a new concept to work with them.

Further my point was that the argument for the existence of infinity could be located precisely in the continuous growing of the value of integer numbers as done in math. I therefore don't see how the very same continuous growing would undermine asserting the concept of infinity to reality.

I don't believe infinity is a logical concept and reality is logical so again the size of the universe is not infinite. — Devans99

I reformulate this as
1) Reality is not logical
2) Conclusion: The size of the universe is not infinite
(feel free to object to my paraphrasing your position if you think I misunderstood you)

I don't understand how you can argue(implication of logic) against or for infinity and assert and value to the conclusion if you take 1) as given.
Even if we dispense this criticism for a while I don't see how you get from 1) to 2) (due to the lack of further steps) without resorting to it being a statement of believe and you being free to believe whatever you want. (I am not opposing this statement and only trying to point out that if you resort to it being a matter of believe there is no point arguing for it.) With this in mind I assume you have a reasonable argument that leads from 1) to 2) that simply isn't spelled out here. So I would appreciate it if you could maybe provide this reasoning in more detail for me to comprehend how you arrive at 2).

This thread is just about if the universe is infinite in size or not. — Devans99

On any understanding of infinite I know of, not infinite. But who claims it is, who is, or whose claim is, worthy of respect in this forum? In the poetic or metaphoric sense wrt the universe, "infinite" just means large, the universe being the largest thing.

But why wrestle this meaning against the rigorous mathematical meaning? "Infinite" in this sense is just a homonym.

I am aware that you can classify infinite sets via cardinal numbers. However calling them numbers seems to me a bit of a stretch. — CaZaNOx

And then some. Numbers have fixed values be they natural, real, matrix etc... Infinity has no fixed value so it cannot be a number.

Further my point was that the argument for the existence of infinity could be located precisely in the continuous growing of the value of integer numbers as done in math. I therefore don't see how the very same continuous growing would undermine asserting the concept of infinity to reality. — CaZaNOx

That would be a Potential Infinity which I do not object to. It is Actual Infinity that I believe does not exist.

I reformulate this as
1) Reality is not logical
2) Conclusion: The size of the universe is not infinite
(feel free to object to my paraphrasing your position if you think I misunderstood you) — CaZaNOx

What I meant was:

1) Reality is logical
2) Infinity is not logical
2) Conclusion: The size of the universe is part of reality so not infinite

In the poetic or metaphoric sense wrt the universe, "infinite" just means large, the universe being the largest thing — tim wood

There is a danger of confusing very large with infinite. That is maybe what has happened to the universe; it is very large so it is convenient to approximate it with infinity and over time this has become a belief that it could actually be infinite in size.

Devans99
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↪Frank Apisa
This thread is just about if the universe is infinite in size or not. Whether the universe was created would be a separate thread. — Devans99

But you have already responded to my question...

...and it appears all you are aiming at is that it is possible that the universe is finite.

I am sure everyone will agree that it is POSSIBLE that the universe is finite...just as it is POSSIBLE that the universe is infinite.

So...all this haggling seems to be unnecessary.

Why not just agree that it is possible the universe is finite...and that it is possible that the universe is infinite?

There doesn't seem to be anywhere to go with resolving the unresolvable.

The point of this thread is to discuss whether the universe is infinite or not and maybe even reach a conclusion.

I am sure everyone will agree that it is POSSIBLE that the universe is finite...just as it is POSSIBLE that the universe is infinite — Frank Apisa

Can you offer any understanding - yours or anyone else's that is not itself fantastical - of just how the universe could be actually infinite?

Keeping in mind that an infinite universe necessarily has infinite yous responding to infinite mes on his thread, with other infinities of you and me in slight variations from this, and so on, & on, & on....

To reduce infinite to possibility is an abuse of "possibility." Just as it would be to assert that it's possible for you to be other than you are. Conceivable, maybe. Possible, how?

tim wood
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I am sure everyone will agree that it is POSSIBLE that the universe is finite...just as it is POSSIBLE that the universe is infinite — Frank Apisa


Can you offer any understanding - yours or anyone else's that is not itself fantastical - of just how the universe could be actually infinite?

Keeping in mind that an infinite universe necessarily has infinite yous responding to infinite mes on his thread, with other infinities of you and me in slight variations from this, and so on, & on, & on....

To reduce infinite to possibility is an abuse of "possibility." Just as it would be to assert that it's possible for you to be other than you are. Conceivable, maybe. Possible, how? — tim wood

By just being what IS, Tim.

IF the universe is infinite...however that is...IS.

If you are saying it is IMPOSSIBLE for the universe to be infinite (and eternal)...you are defying logic. Of course it is POSSIBLE. And, if the probability or likelihood were a gazillion to 1 against...it remains POSSIBLE.

And if that happens to be infinite...it just IS.

Are you arguing that it is IMPOSSIBLE that the universe is infinite? If so, the burden of proof would fall on you...not me.

— Devans99

Cop out...but I understand.

Well it is impossible for the universe to be infinite in size:

- Size is a number
- Infinity is not a number
- So the universe is not infinite in size

I understand Newtonian physics very well but when you get into the most modern physics there are critical details i'm not aware of so i don't want to make it out like this is a complete answer.

That being said if there is an infinite amount of area for matter and energy to expand into my logic circuits tell me there is an infinite amount of space. Without a doubt i am missing something.

My view is that spacetime started with the Big Bang 13 billion years ago and is expanding into 'nothingness' - no time / no space.

Nothingness itself cannot be said to be infinite (because it is nothing, it has no dimensions).

"Nothingness itself cannot be said to be infinite (because it is nothing, it has no dimensions)."

i have no evidence to say your wrong. This is one of those things that i would have to study for 2 months.

1) Reality is logical
2) Infinity is not logical
2) Conclusion: The size of the universe is part of reality so not infinite — Devans99

Nitpicking, I'd say ...

1. we employ logic to understand reality
has served us well; for that matter, meaning presupposes identity

2. if ∞ derives a contradiction, then ∞ is illogical
and this is not the case in general; we have some examples of veridical paradoxes, which goes to show that ∞ can have counter-intuitive implications, and that's not the same as illogical; that said, there are some cases where we take a derived ∞ to indicate a problem; dealing with ∞ requires special care

3. who knows what exactly is real or not; reality does not have to abide by our thinking

- Infinity is not a number — Devans99

∞ ∉ R (not among the reals, requires different treatment)

∞ requires special care, different treatment than our usual numbers, sort of like a quantity that's not a number.

2. if ∞ derives a contradiction, then ∞ is illogical
and this is not the case in general; we have some examples of veridical paradoxes, which goes to show that ∞ can have counter-intuitive implications, and that's not the same as illogical; that said, there are some cases where we take a derived ∞ to indicate a problem; dealing with ∞ requires special care — jorndoe

My opinion is that the very conception of infinity is illogical. ∞+1=∞ implies the existence of something that when it is changed, it does not change. That is deeply illogical.

∞ ∉ R (not among the reals, requires different treatment) — jorndoe

My argument is that if infinity was a number X, then X would be greater than all other numbers. But X+1>X. So infinity is not a number.

If you are saying it is IMPOSSIBLE for the universe to be infinite (and eternal)...you are defying logic. — Frank Apisa

I don't think so. I think what you mean is unbounded. As the surface of a sphere is unbounded - but by no means infinite. So yes. The universe is not infinite. And that is logic, not a defiance thereof. Perhaps you're confusing logical possibility with conceivable possibility - anything is conceivable.

Stop for a moment and think bout what "infinite" means.

tim wood
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If you are saying it is IMPOSSIBLE for the universe to be infinite (and eternal)...you are defying logic. — Frank Apisa


I don't think so. I think what you mean is unbounded. As the surface of a sphere is unbounded - but by no means infinite. So yes. The universe is not infinite. And that is logic, not a defiance thereof. Perhaps you're confusing logical possibility with conceivable possibility - anything is conceivable.

Stop for a moment and think bout what "infinite" means. — tim wood

If you are saying it is impossible that the universe is infinite...you are simply sharing a blind guess about the reality.

To assign it logic is an absurdity.

But...even if the point were conceded...where do we go from there.

↪Frank Apisa
Well it is impossible for the universe to be infinite in size:

- Size is a number
- Infinity is not a number
- So the universe is not infinite in size — Devans99

Size is not always a number.

We talked about that.

But take the word size out if you must.

Are you saying it is impossible for the universe to be infinite?

You've been on both sides of that question...I'm just wonder if you want to stick with one side or the other.

∞+1=∞ — Devans99

... is illogical.
As mentioned, ∞ is not just one of your ordinary numbers, that you can stuff into ordinary arithmetic.
That would be the illogical part, not ∞.

'' 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.''

Could it be argued that since the universe is all we know and nothing exists outside of it by definition, it can't be enclosed by anything larger than it. So in a sense it would be the ultimate infinity and not part of a subset. Since the universe is expanding, using OP's argument that "if it was size X, it is now size X+1, meaning X was not infinite", then the universe by definition is finite.

@Devans99, https://en.wikipedia.org/wiki/Koch_snowflake

A line that extends to infinity, contained within a circle of fixed area.

Now, suppose the circle was expanding, and taking the Kotch Snowflake with it....

A Koch snowflake always has a finite perimeter length, the process that produces them is an example of Potential Infinity. If a Koch snowflake existed in reality it would have a finite perimeter (because matter is discrete). Does not matter how far you expand the snowflake, it still has a finite perimeter.

Of course, a Koch Snowflake has an infinitely long perimeter. What you are saying is that such a snowflake cannot be constructed with matter, because matter is discrete (or some such...).

And hence this shows your odd notion of "exists". As if, despite our being able to talk about them, you were to say that there is no such thing as a Koch Snowflake.

My suggestion is that what has led you to rejecting the mathematics of infinity is just such a confusion.

...using OP's argument that X+1>X, — curiousnewbie

What he said was:

(if it was size X, it is now size X+1, meaning X was not infinite) — Devans99

Which is just false. Infinity plus one is still infinity.

What you propose here is quite different.

There is a difference between what can exist in our minds and in reality. In our minds it is perfectly possible to construct illogical things that can't exist. For example I can imagine a talking tree. Just the act of imagining something does not make it potentially real. To be potentially real, the object has to be realisable and logical.

Infinity is not realisable - its not possible to construct anything infinite in size (you would never finish)
Infinity is not logical - see above comments in previous posts.

What he said was:
(if it was size X, it is now size X+1, meaning X was not infinite)
— Devans99

Which is just false. Infinity plus one is still infinity. — Banno

But expansion says there exists a number X+1 (the new size) that is greater than X (the old size). So how exactly can X be infinite?

Anyway:

- ∞+1=∞ explicitly says infinity can't expand.
- Infinity is unmeasurable so it has no size so it can't expand.
- Infinity does not exist.

Devans99

A Koch snowflake always has a finite perimeter length, the process that produces them is an example of Potential Infinity. If a Koch snowflake existed in reality it would have a finite perimeter (because matter is discrete). Does not matter how far you expand the snowflake, it still has a finite perimeter. — Devans99

Whether or not matter is discrete is still in contention...and probably will be for a very long time.

Atoms were once thought to be the ultimate smallest thing.

Using "matter is discrete" as part of the argument for "the universe is finite" is essentially using a guess...which allows for the possibility that the universe IS infinite. (But of course, we all already realize that.)

Whether or not matter is discrete is still in contention...and probably will be for a very long time. — Frank Apisa

Are you suggesting a never-ending faberge egg style arrangement with an unending sequence of smaller and smaller sub-atomic particles?

Or are you suggesting we will discover a sub-atomic particle that is continuous (IE infinity divisible)?

Both seem rather far fetched so I lean heavily towards matter being discrete.

Devans99
1.1k

Whether or not matter is discrete is still in contention...and probably will be for a very long time. — Frank Apisa


Are you suggesting a never-ending faberge egg style arrangement with an unending sequence of smaller and smaller sub-atomic particles?

Or are you suggesting we will discover a sub-atomic particle that is continuous (IE infinity divisible)? — Devans99

I am not suggesting anything, Devans.

I am stating as an absolute fact that the question of whether matter is discrete or continuous...has not been answered absolutely. And then I am speculating that it will be a LONG TIME before it is...if ever.

...using OP's argument that X+1>X, — curiousnewbie


What he said was:

(if it was size X, it is now size X+1, meaning X was not infinite) — Devans99


Which is just false. Infinity plus one is still infinity.

What you propose here is quite different. — Banno

You are correct, what I worded was different to what OP actually said. I did that out of sheer laziness, will edit it.

if i add 1 + 1 + 1 + 1 that is 4. If i do the same thing again that is 8. If i die tommorow and never do this process again and at the same time have never heard of the term 12 i might conclude that `12 doesn't exist. The problem is our ability to testify what we believe is true is limited by our time on this earth. Infinte is not necessarily a fake construct its just we personally only have a limited time to testify to the things we hold to be true. If the universe keeps expanding i believe it is certainly possible that it could expand to twice as big, three times as big, 4 times as big and so on.