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"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.

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."

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.

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.

It has been quite studied in math, in the theory of Alephs (https://en.wikipedia.org/wiki/Aleph_number) (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".

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!

Sorry, Plato sucks. Long live Aristoteles.

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.

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.  ;D

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.

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.



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.

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.

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.


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

No, it is jus mo'biggaa




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  ;D


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.

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".

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.

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)


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

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...

Makes you wonder, if the universe in finite, what lies beyond?  My mind just can't fathom it.  :/

"It's no use, Mr. Vod — it's turtles all the way down!"

Surely though, the universe includes everything that exists. If something did lie beyond it, that something would have to exist, and therefore would be part of the universe.

Indeed, nor mine. I cannot conceive nothingness... at most void which in itself occupies a volume even if empty. I just try to be humble and believe that there are things that are true even if I can´t think of them.


At the risk of going full speed into philosophical nonsense, as things are today our universe is limited to what we can perceive, and that is very, very limited.

Infinity is something which doesn't have any boundaries on either side and extending to some non-explainable distances or something which has a greater value than a normal natural number. The size of the universe cannot be theoretically measured as radiations sent from earth reached back and there is still more space to explore beyond the distances. Thus it can be said that universe has an infinite size nor it can never be measured with current technological instruments. Even the size of the observable universe/cosmic web is unfathomably large. So it's better to stay on the point that whole universe can never be measured and can be considered as an infinite area of black space, galaxies, super clusters all held together by gravity.

Even if we create a module or a space probe which can travel at the speed of light (better than a Millennium Falcon  ;D), it would take you 45 billion light years to reach the end of cosmic web. Considering the Big Bang happened before 14 billion years, the light emitted from galaxies created 14 billion years ago took 14 billion years to reach the earth and also they are expanding at a rapid phase which might have doubled putting the radius to 46 billion.  Isn't this number beyond a natural number? I assume that if scientists find a way to travel through the black hole, it may take us to the other end of the universe or something beyond the infinity. Also they believe that the whole universe is 10²³ times larger than the current observable universe.  :o These numbers would just bring us nightmares if we think of what is exactly the size of the whole universe?

Endless?  ??? What do you mean exactly by the term endless? We start at a point and end at the same point, this isn't endless! Endless is which doesn't have a end point and you never able to reach the end point.

I don't think that's true. Until recently we couldn't perceive or measure the Higgs boson, only theorize its existence. That didn't mean it was any less part of the universe.

It may be part of someones universe, but not of yours until you can "see it" (or demonstrate it, or perceive it). Universe is not objective. (Full speed now into phi... I never learn)/


Nope, even you can't "see" the limit, you can calculate a limit by inferring it from the age of the universe and the speed of its expansion, so it can be (and it has already been) theoretically measured.

Your assertion refers only to the Observable Universe AKA Hubble Volume

You are all very terrible at mathematics. Everyone here should stop this discussion immediately. Please save yourself from embarrassment. This thread is very cringy. Please stop it and please pick up a book and read it.

If infinity is circular, there must be something outside the circle.

To get a good grasp of infinity and the different levels of infinity, please pick up a basic book on set theory and read it (to make it accessible, you should know propositional logic, predicate logic, and). You will need to grasp concepts such as the ZFC axioms, the proof of Zorn's Lemma from AC, cardinals (you should be able to immediately tell the cardinality of objects (with a proof) such as a the complex number plane, the set of all ultrafilters on N, any compact second countable space without isolated points, the set of all strings over a finite or countable alphabet etc.), well-ordered sets, ordinals (including transfinite induction), ordinal arithmetic, basic cardinal arithmetic, inaccessible cardinals (you could go further and read up on all large cardinals), surreal numbers, and non-standard analysis. Until you understand these objects, there is no point of rambling all sorts of nonsense about infinity.

I immediately thought about positive amd negative infinities.

Like a Cartesian plane. You can have lines that tend to infinity in different directions.


https://1.bp.blogspot.com/-Z6FOTw8hSZs/UB8mU0EPAKI/AAAAAAAAALk/eykbEq7ZLc0/s1600/500px-Hyperbola_one_over_x.svg.png

The universe is flat, just like the earth ;D.

---

Onto this, I’ve been taught set theory for the third time and in it they were proving that the length of the set of natural numbers is less than the length of the set of irrational numbers. The length of the natural numbers is given a certain name to mean infinity, the set of irrational numbers is 2 to the power of the number of natural numbers that exit (making a very huge number).

So there is something beyond infinity as it is just a variable intentially undefined (or at least badly defined).

That's where the omnipotent the sky fairy god of the gaps hangs out.
Fuck knows what he was doing for the infinite amount of time that passed before he decided to
zap the earth into being, like about 6000 years ago....

But seriously...
Think of the 2d surface of a sphere.... its finite but unbounded.
The universe is kinda like that, but in 3D, (well 4D if you include time ,then its space time, but that's another topic) finite but unbounded.
Yeah...my mind cannot fathom it either, I like this topic though.

All that talk about multiple inifinities in mathematical sense is a talk about cardinal numbers. They are used to talk about the size of sets and to compare sizes of infinite sets in particular. You cannot actually go into a size of set, and you cannot go "beyond" that either. So they are of little use in that particular sense.

I would rather think about "crossing infinity" differently and here is how:

What I immediately thought about when I read the thread title was something like moving "through"  assymptotic lines. Imagine you have a two dimensional chart like that one:

https://i2.wp.com/blog.etrapez.pl/wp-content/uploads/2010/09/Picture72.png?w=764&ssl=1

Now, imagine you are moving up - moving across Y. Passing through point y=a means you pass "through" an asymptote and you immediately find yourself beyond infinity in the second dimension, i.e. in X.

This is the same as passing through the black hole "event horizon". It takes infinitely long etc. so it is not easy to do - but when done, voila: you are beyond infinity. Congratulations!

Black holes and the event horizon are unrelated to mathematical infinite or any other concept of infinite.



Your conception of infinite is quite limited to maths. Have you considered that this thread is NOT about math?



Thank the gods of Olympus that you are here to tell us  ;D ;D  I just hope that you know a bit more about math than about physics....

Paxmao.

I hate to break it to you, but without exceedingly difficult modern mathematics, one cannot get beyond a childish understanding of the infinite. But this understanding of the infinite requires something called WORK that comes at a very high price. And your childish nature is showing through your nonsensical ad-hominem attacks. Grow up. Please do not talk to me until you multiply the ordinals (w+1)*(w*2+3)*(w*7+16). If you are unable to multiply the ordinals, then you should not talk about infinity at all. I am better than you.

P.S. As for the other thread, I was not trying to imply that my scenario was in any way likely. I was simply trying to ask a philosophical question since time reversal is a phenomenon that occurs in the universe critters. And yes, critters does exhibit the second law of thermodynamics and time reversals.

Sufficient to say that you are able to accuse me of personally attacking you while your are personally attacking me in the same sentence, all after having attacked personally everyone that participated on this thread, and then consider yourself better on your own selection of a test and what is funnier "more mature" (that, at my age, is something to avoid). That reveals everything that needs to be known about you.

Please, consider me bored already.


Have you got a credible source stating that as a proven fact or you consider yourself of such a grandeur that proof´s not needed if you say something?



Speaking of childish. Please, consider yourself better at multiplying ordinals than me. I can live with that - I accepted long ago that math requires much more time and produces much less results than other disciplines. Enjoy.

P.S. care to correctly insert the symbol for omega or mention that you are using a "w" instead, someone that does not know what you are talking about would not understand your question.

P.S.S. I am going to use that question it in my next Weekly Merit contest in the Spanish section to see what people answer. I am intrigued to know what you consider difficult.

Paxmao. Please demonstrate that you have intelligence by multiplying the ordinals (w+1)*(w*2+3)*(w*7+16). I usually do not communicate with people who cannot demonstrate their intelligence. Your hatred of mathematics is a sign of your mental deficiency. I am still better than you. You are a troll.

I am still waiting for your source reference regarding the "symmetry of the universe", mature one. Unless you consider that trolling (thin skin for a such a quarrelsome individual, reminds me of Sheldon Cooper) - in your language "Using the classification of an individual into an undesirable group to refute its argument does not diminish the truth in it".

I don´t know the answer to that question. The reason for that is that I am not interested in knowing it, since it would imply using my time learning something that is irrelevant for me.

I am going to use the last 5 minutes  that I can waste with you for this month just to inform you of some misconceptions you have about life:

Your conception: Being smarted is knowing more maths.
Reality check: Being smart is choosing carefully how to use your time. Hint: Maths that you don´t need are most likely the wrong answer.
 
Your conception: Being "smart" is the most important thing.
Reality check: Being emotional intelligent will take you further (https://www.huffingtonpost.com/entry/iq-versus-eq-emotional-intelligence-in-the-workplace_us_5a56590be4b024fa0543b62d).

Your conception: If I challenge paxmao on a forum and he does not answer I have proven my point (being "better"?).
Reality check: paxmao´s ego does not depend on answering your question nor I feel threatened for you own opinion about yourself.

I encourage everyone, including you to participate in my next Weekly Merit contest. It is in Spanish for the moment, but I may make a English edition.

I bet you are fun at parties.

Pax Meow. You still did not multiply the ordinals (w+1)*(w*2+3)*(w*7+16). The ordinal multiplication problem is a type of problem known as a proof-of-work problem which I use to decide whether I should have an intelligent conversation with you or to conclude that I am better than you.

You sure it wasn't her that was doing the "walking out"?

Algebra. The most potent of aphrodisiacs.

;D they probably assumed it was a joke oeleo.
@jvan, are you single? I’m thinking you must be but maybe you found someone?

I’d like the problem to be translated into reverse Polish notation also, then we can do away with out the brackets and it becomes more clear what you want as you could well be a bot.

Does it matter if she was the one walking out? If someone is not intelligent enough to solve a math problem, then it does not deserve my attention.

I am not going to tell you if I am single or not because your name is JACK which means that you are a dude and I am not interested in dudes. I will only reveal my status if the person asking is female has demonstrated interest by solving one of the math problems that I give her.

As for the reverse polish notation, here it is: w1+w2*3+*w7*16+*. Since you asked for reverse Polish notation, I suppose that you want to solve the problem? And why do you want to solve a problem in reverse Polish notation when the operations in question are both associative and where you are a human and not a calculator?

Have you accepted the Lord Jesus Christ as your personal Lord, Savior, and Saviour?

1. It also says it on my profile.
2. Good because I wasn't asking you (and neither am I).

Reverse polish looks a lot nice, furthermore it means I can do this.
1. Type error with context of ordinals due to mixture of variables, running exception statements
2. Add w to stack
3. Add 1 to stack
4. Pop them and add 1+w to the stack (not how it would be represented but humour me)
5. Add w to the stack
6. Add 2 to the stack.
7. Pop them and multiply the outputs to the stack (2w).
8. Pop last item and add 3
9. POP AND MULTIPLY!!!!!
10. Add w to the stack
11. Add 7 to the stack
12. POP AND MULTIPLY
13. pop and add 16
14. Multiply (oh fuck) 14w³+67w²+101w+48

(Sorry, I appear to have had more of a fiddle then I'd intended to. Anything more I can help you with?

dy/dx = 42w²+134w+101
d2y/dx2 = 84w+134
d3y/dx3 = 84
d4y/dx4 = 0
first integral = 3.5w⁴+22.333...w³+50.5w²+48w
second integral = 0.5w⁵+5.583325w⁴+16.833...w³+24w²



You're a turing machine with a stuck tape? Is that what you mean to tell us. It might be a flipflop issue with the head maybe you should get someone to check it out?

Jack. Nice try with the multiplication (I give you an 'F-' for eFFort) . . . except for a couple things.

1. Ordinal addition and multiplication are not commutative. For example 1+w=w but w+1>w and 2*w=w but w*2>w. As written, your answer would simplify to w^3+w^2+w+48.*

2. Ordinal arithmetic does not satisfy two sided distributivity. Ordinal arithmetic satisfies the distributivity law a*(b+c)=a*b+a*c, but
(w+1)*2=w+1+w+1=w+w+1=w*2+1 but w*2+1*2=w*2+2, so (w+1)*2<w*2+1*2. *

3. Taking derivatives of ordinals does not make any sense since ordinals are not polynomials.

4. Taking integrals of ordinals does not make any sense either since ordinals are not polynomials.

5. You need to capitalize the letter 'T' in Turing.

6. In ordinal arithmetic, there are no fractions or decimals. 3.5 does not make any sense in ordinal arithmetic.**

*-Actually, there are operations on the collection of ordinals which are called natural addition and natural multiplication. Natural addition and natural multiplication form a semiring. In other words, these operations are associative, commutative, and they satisfy the two-sided distributivity property x*(y+z)=x*y+x*z. Because having only one kind of ordinal addition and multiplication is not enough.

**-If you use the natural operations on ordinal arithmetic, then you can extend the class sized semiring of all ordinals to a field called the field of surreal numbers which contains all real numbers, ordinals, and other critters. The point is that in the field of surreal numbers, you actually can multiply ordinals by real numbers.

You’ve managed to somewhat confuse the terms ordinal and discrete into a horrible fashion. Maybe take a look, at that?

A question answered badly is one which was asked badly when the questioner is less intelligent than the answered such as in this case.



Checking google,
Ordinal ::= {x = N /\ 0<x<11}

You clearly do not know what ordinals are. I asked a perfectly reasonable question, but your mathematical knowledge is deficient. That is very sad. It is a greater tragedy than Hans Christian Andersen's "The Little Mermaid" (I am not talking about the Disney version. You can tell that the Disney version of The Little Mermaid is watered down because you never see nipples on the mermaids because their breasts are covered with seashells). You need Jesus.

My conclusion reading this thread is that there are three types of users: Those who can count and those who can´t.

It's not necessary what we see is always true, because behind every "presented" truth, there is a possibly different reality. Just like that, IMHO, nobody in this world can define infinity as well as its limits (because it's unlimited, and if it's not, then it's not infinity). So basically, if something that doesn't have any limits, how could there be something "beyond" it? I'm talking out of the box as I'm nowhere interested into talking math here.


Which one are the type 3?  ;D

oooooh, a nerd pissing match. This is gonna get good!

https://media.giphy.com/media/HZyJ2cLzPRtYs/giphy.gif

Could you do me a favor and solve this math problem before you get out the popcorn so that you have demonstrated that you have the intellectual capacity to appreciate what I have to say (the other people commenting on this thread are simply blathering nonsensical utterances)? Using ultrafilters, prove that for each function f:[N]^2-->2 where N denotes the set of natural numbers, there exists an infinite subset A of N where f is constant on [A]^2 (here [X]^2 denotes the set of all ordered pairs (x,y) where both x and y belong to X). Have you accepted the Lord Jesus Christ as your personal Lord, Savior, and Saviour? Because you certainly act like you hate God.

Sure. Give the next guy the easier maths problem...

Go solve this problem: Show that if there exists a rank-into-rank cardinal, then the free self-distributive algebra on any number of generators can be embedded into an infinite product of finite self-distributive algebras.

I don´t know, I am on the second group.

I have the intellectual capacity to appreciate that nobody here cares about your math problem or your mathematical abilities or your religious superstitions.

I hope you know that your comment demonstrates that you have neither the intelligence that comes with mathematics nor the moral virtues that come by accepting the Lord Jesus Christ as your own personal Lord, Savior, and Saviour. That is sad. Please accept the Lord Jesus Christ as your Lord, Savior, and Saviour, and please pick up a mathematics book, read it, and do some problems. You are pathetic. I thought atheists were smart. It looks like there are exceptions though. I am thankful that my fellow Republicans created cigarettes to get rid of atheists.