To infinity and beyond. Does "beyond" exist ?

[xtraelv]

"To infinity and beyond" was a quote by buzz lightyear.

I have been having a discussion with my wife for a number of days now.

Her position:

There is no "beyond" infinity.

Infinity is infinite. There is no beginning and no end to infinity.
She claims the statement makes no sense.



My position:

There are multiple infinities. Each one larger than the previous infinity.

https://www.science.org.au/curious/everything-else/beyond-infinity

Also by defining "infinity" as having "no beginning and no end" it is limiting infinity.

It means that it specifically excludes beginnings and ends.  So "beyond infinity" would be a beginning or end.


Alternate position:

According to Aristotle, actual infinities cannot exist because they are paradoxical.

To infinity and beyond is a double paradox.

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[o_e_l_e_o]

You might be interested to look in to the work of mathematician Georg Cantor. There's also a great Numberphile video about infinities here: https://youtu.be/elvOZm0d4H0

Mathematically speaking, your position is correct. There are different types and different sizes of infinity. Some infinities are larger than others. You can absolutely have "beyond infinity".

A quote I once heard (I don't remember from where): "There are infinite real numbers between 1 and 2. None of them are 3."

[odolvlobo]

Here is my take...

Infinity is not a number or a place, so you can't go "to infinity" in the first place.
Infinity is a concept, so there can be a "beyond infinity", depending on how you define "beyond" and "infinity".

BTW, while we're on the subject, a dimension is also not a place, so you can't go to or come from a dimension.

[NeuroticFish]

One could also think of infinity as a target. One "dumb" definition of Infinity is that no matter how far you are counting, you cannot reach infinity. And this makes it a "moving target" where nothing can be beyond it.

Then there is the paradox that Cardinal(Natural Numbers) < Cardinal(Real Numbers), and since there are 2 types of infinity, clearly one is beyond the other.


I think that you two can argue as much as you want, but in fact both of you are right; it depends on how you see the things, really.

[paxmao]

...
 it depends on how you see the things, really.

It has been quite studied in math, in the theory of Alephs (the infinite is called an Aleph). Infinites can be of different "orders" and you can actually divide two Alephs and find out that the result is infinite or zero or any real number.

Example:

A=X^3 is infinite when X= infinite, B=2X is also infinite when X is infinite. However,  if you divide B/A the result will be zero. Even both A and B are infinite, there are not the same type (order) of infinite.

Now, let C=3X^3, then if X= infinite C/A = 3

Now, is there anything beyond infinite? In my view, the first question we should ask is "Is infinite anything but a logical concept?" That is, I can conceive logically and infinite as the cardinal of N, the number of real numbers between 2 and 3 or the result of dividing 1 by 0, etc... but... Does the fact that I can it conceive make it real? Cannot I conceive a flying elephant or a forum without spam, yet these are not real?

If you can answer that, then we may progress on to "beyond".

[acmakc12]

In an infinite number of parallel universes, it makes perfect sense.. but in an infinite number of alternate parallel universes, it doesn’t make sense. Here’s the kicker, since “half of infinity” is also infinity, that means it makes sense but it doesn’t, at the same time.

The physical is absolutely meaningless and insignificant without that which is beyond it. The physical is the finite whereas that which animates and gives it meaning is infinite.
The physical is merely the dance of  the Infinite and we are this dance!

[paxmao]

The physical is merely the dance of  the Infinite and we are this dance!

Sorry, Plato sucks. Long live Aristoteles.

[SaltySpitoon]

It has been quite studied in math, in the theory of Alephs (the infinite is called an Aleph). Infinites can be of different "orders" and you can actually divide two Alephs and find out that the result is infinite or zero or any real number.

Example:

A=X^3 is infinite when X= infinite, B=2X is also infinite when X is infinite. However,  if you divide B/A the result will be zero. Even both A and B are infinite, there are not the same type (order) of infinite.

Now, let C=3X^3, then if X= infinite C/A = 3

Now, is there anything beyond infinite? In my view, the first question we should ask is "Is infinite anything but a logical concept?" That is, I can conceive logically and infinite as the cardinal of N, the number of real numbers between 2 and 3 or the result of dividing 1 by 0, etc... but... Does the fact that I can it conceive make it real? Cannot I conceive a flying elephant or a forum without spam, yet these are not real?

If you can answer that, then we may progress on to "beyond".

Your explanation is a little misleading. Your understanding of limits isn't wrong, but the application is. When you say A = X^3 and C = 3X^3, if you take C/A you get 3, that is the case as X approaches infinity, not when it is at the value infinity. The reason you can express the limit of the function 3X^3/X^3 = 3 as X approaches infinity is because on the way up from your lower bound to infinity, the magnitude of the numerator is growing at a rate 3 times greater than the denominator. That is the domain includes all real numbers from negative infinity to positive infinity, non inclusive. If you try and deal with the value infinity, you almost always get some sort of undefined function because infinity isn't a number.

You can't go beyond infinity, because you can't reach infinity. Even if you say, infinity + 1, since infinity isn't a number, that makes about as much sense as saying, green +1.

[Vod]

Infinity is infinite. There is no beginning and no end to infinity.
She claims the statement makes no sense.

I agree with your wife.

It's just an exaggeration like "I gave 110%".   That statement makes no sense either - as 100% defines the maximum you can give.

[xtraelv]

Infinity is infinite. There is no beginning and no end to infinity.
She claims the statement makes no sense.

I agree with your wife.

It's just an exaggeration like "I gave 110%".   That statement makes no sense either - as 100% defines the maximum you can give.

I won't hold it against you. 

[Elqui]

The beyond can mean differently and depends on how someone interprets it. For me beyond infinity is more than forever. I think it makes something more than infinity.

[r1s2g3]

The simplest concept I know about infinity is that something that you cannot measure at all. So saying something beyond infinity is just applying a superlative degree and just a verbiage.
Actually , infinity is also relative. Movement of electron to infinity will not be same distance  to the movement of human being to infinity.
So what exist as infinity for object A will not be infinity for object B.

There are multiple infinities. Each one larger than the previous infinity.

When we are not able to measure infinity, how we conclude that other infinity is larger than first infinity?
In reality, with our advancement our definition of infinity is changing. What was not measurable yesterday (tends to infinity/infinity) is measurable today and next non measurable thing become infinity for us today.

[mu_enrico]

"To infinity and beyond" was a quote by buzz lightyear.

I think this quote does make sense, for example, the infinite number usually used to describe something uncountable, like the number of sand in this universe.
What if there are multiple universes? What if there are infinite numbers of universes? Isn't that makes the sand in the different universes become "beyond infinity"?
Never mind, I'm just slamming my head on the table while writing this post.

[Mpamaegbu]

The syllogism, "No man dies to himself" puts a huge question mark on the theory of Infinity. Where your being stops, there's another's starting immediately. There is nothing truly as something being infinite in the real sense of it. Something must intercept that abstractness one way or the other. At a point it terminates. Nothing lasts forever. Even from the Christian faith, the Bible talks about a certain destruction of the world at a certain time to come and a new world emanating.

It's just an exaggeration like "I gave 110%".   That statement makes no sense either - as 100% defines the maximum you can give.

Yah, it's like saying something is more original than the other. If it's original, it's original. Simple and short.

[paxmao]

...
What if there are multiple universes? What if there are infinite numbers of universes? Isn't that makes the sand in the different universes become "beyond infinity"?
...

No, it is jus mo'biggaa

Infinity is infinite. There is no beginning and no end to infinity.
She claims the statement makes no sense.

I agree with your wife.

It's just an exaggeration like "I gave 110%".   That statement makes no sense either - as 100% defines the maximum you can give.

Aggg... I was struggling about arguing about this, as the discussion is going to be pointless.... but nobody said 100% of the maximum he can give, it may be 100% of what he was expecting to give  

...

Now, let C=3X^3, then if X= infinite C/A = 3
...

Your explanation is a little misleading. Your understanding of limits isn't wrong, but the application is. When you say A = X^3 and C = 3X^3, if you take C/A you get 3, that is the case as X approaches infinity...

You are describing the concept of the limit of a function. Your assertions are correct in that respect and I fully accept that I have not been accurate, in my attempt to simplify.

However, operations with infinities as concepts are not undefined, that is what the theory of Alephs studies.

[jonemil24]

Math can sometimes be hard to express in language. "Infinity and beyond" can be an exaggeration, but math will always have its way to prove it.

The universe is infinite, it's always what we(or it could only be me) know of. I don't remember how I learned about it, but this topic gave me an odd idea.

There is theory about expanding universe which I "somehow" compare on "how we used to live" on our own planet. If we go further east; it'll be west, of course, same as north to south. Then it dawned on me, could our universe be just a "loop"? If we go further the universe, no matter what direction and without turning back, we will comeback to where we also started. The infinity also looks like a loop to me.

If the universe is proven to be just an endless loop, it's about time to prove the parallel universe's existence.

I'm not great with math, I only know about the basics of it. The infinity+1 or "beyond infinity" is acceptable if infinity is just an endless loop. But the "time is but a stubborn illusion" quote from Einstein is hard to accept and comprehend, since everything is associated with time.

[xtraelv]

Math can sometimes be hard to express in language. "Infinity and beyond" can be an exaggeration, but math will always have its way to prove it.

The universe is infinite, it's always what we(or it could only be me) know of. I don't remember how I learned about it, but this topic gave me an odd idea.

There is theory about expanding universe which I "somehow" compare on "how we used to live" on our own planet. If we go further east; it'll be west, of course, same as north to south. Then it dawned on me, could our universe be just a "loop"? If we go further the universe, no matter what direction and without turning back, we will comeback to where we also started. The infinity also looks like a loop to me.

If the universe is proven to be just an endless loop, it's about time to prove the parallel universe's existence.

I'm not great with math, I only know about the basics of it. The infinity+1 or "beyond infinity" is acceptable if infinity is just an endless loop. But the "time is but a stubborn illusion" quote from Einstein is hard to accept and comprehend, since everything is associated with time.

It really does depend on how you define infinity.

Whether it is actual infinity, mathematical infinity or theoretical / philosophical infinity.

I am now of the opinion that we are both correct and both wrong. Depending on the definition used of infinity.

Taking the definition that infinity is forever infinite. It means that it has no start and no end. Yet by definition of "infinate" it will have "infinite starts and infinite ends"

This means that infinity contradicts itself and has infinite contradictions. So "beyond infinity" would be where it doesn't contradict itself.

With theoretical infinity it doesn't matter whether it can exist or not. Because it is a theoretical "infinity" and therefore theoretical "beyond infinity".

[chriskaos6669]

The earth is round. So endless.

Infinity is the same circle. If you go beyond the boundaries of infinity, you will go beyond the boundaries of the circle, and you will enter another infinity.

[paxmao]

Yet by definition of "infinate" it will have "infinite starts and infinite ends"

I don´t see how you reach that conclusión from the definition. IMO being able to "loop" on an object does not mean that it is infinite. You do infinite loops or walk infinite miles on it, but all the dimensions of the object are finite ( it does not have to be a circle, it can be any closed polygon)

...

The universe is infinite, it's always what we(or it could only be me) know of. I don't remember how I learned about it, but this topic gave me an odd idea.

There is no particular proof of the universe being infinite. Theories, AFAIK, are mostly pointing to the opposite.

[BeBlockTech]

Infinity is infinite. There is no beginning and no end to infinity.
She claims the statement makes no sense.

I agree with your wife.

It's just an exaggeration like "I gave 110%".   That statement makes no sense either - as 100% defines the maximum you can give.

I'm gonna have to agree with his lady on this one. Infinity is what it says, "infinity", don't think you can go beyond that. I do think you can go beyond immortality though, but that's for another topic...