Question Can one infinity be larger than another infinity?

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" It is a mathematical invention which is useful (?) in mathematics but no use for anything else."
So, you want to be a mathematician - all the best.
I did quite a lot of maths in my chem eng course.

Give me one example where you can use the word (or related adjective etc) in everyday life where it is not just an exaggeration such as "that was infinitely good".

Cat
I might be in a grey area here, but just for the interest of everyone, how about these.

Many adjustments are infinitely variable, volume, temperature, pressure, tuning radios etc.

Many gadgets and things are infinitely adjustable; reclining car seats are described as infinity adjustable, anything with a screw adjustment is infinitely adjustable such as a lathe, a focusing mechanism etc.

Some musical instruments have infinitely adjustable tones or notes.

Measuring instruments – thermometers, altimeter, barometer pressure sensor, strain gauge have infinitely smooth progressive readouts.

A ball thrown in the air will stay at its maximum height for an infinitely small time before falling, same with a piston (it has to stop before reversing).

The centre line of a smoothly moving clock hand will remain on the centre line of the hour mark for an infinitely small amount of time.
 
I think Cat came closest.

Infinity is a concept. It's not a value that can be acted upon in mathematics. There is no "Positive Infinity" or "Negative Infinity". You cannot assign value, add to or subtract from infinity. The closest you can get is attempting to divide by zero.

-Wolf sends
I think maths does include +ve and -ve infinity as per statement;

-∞ < x < ∞ where X is a real number.
 
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Sorry, but I think you're mistaken here. If you can continue to subtract a value, then you're not starting at infinity and you're not ending at infinity because you can ALWAYS subtract one more. If you can continue to add a value, you're not starting at infinity and you're not ending at infinity because you can ALWAYS add one more.

Again, Infinity is a concept; not a value that can be acted upon.

-Wolf sends
2 different things here, yes you can't add or subtract to infinity but you can assign it + or - value.
 
Indian Genius

You are a very clever person. Infinity has nothing to do with reality. Stop trying to add or subtract from it. Infinity is just something useful in mathematics. Leave it alone when discussing reality. That is my advice from a long life. A life dedicated to science and knowledge.
My 'hobby' has been the study from the BB or 'before the BB, through astronomy and planetary sciences to the solids we stand on - geology.
I have advices for you which will appear as needed in these discussions.
Do not worry about the mental construct - infinity - leave that alone.

Cat :)
Embrace infinity! maths needs infinity, science needs maths, space needs maths. this is a space website.

Don't let anyone dampen your enthusiasm, maths is fun, even for its own sake.
 

Catastrophe

The devil is in the detail
This is my last word on the subject:

Thought experiments can be (as in this case) like dreaming about the lottery. What if I won.

Here is a real science example for you.
Two light beams coming towards you, each at the speed of light, have a relative velocity of 1 c not 2c.

Similarly, 2 x infinity = 1 x infinity. Q. E. D.

I wish you all the best, but I am not wasting my life posting about (IMHO) absurdities.

I am G O N E


Cat :) :)
 
Lets pretend we have 2 universes separated forever with no interaction whatsoever.
Each one for all practicality is infinity.
If they can merge, bounce off each other, gravity interact, cannibalize each other or any other form of interaction then we have 1 infinity.
JMO
 
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"Can one infinity be larger than another?" Noted mathematician Georg Cantor effectively answered that question long ago. The answer was "yes" and it's called "proportionality." Things that are naturally proportional in the finite will also be naturally proportional to infinity. In other words, to an infinity of universes (u) proportionality will simply continue proportionally.. Something like energy always being conserved, thus causing an infinity of less relative to non-relative universes (u) to exist rather than any infinite of energy possibly existing, proportionality will also always be conserved across the board (in and of an infinity of finite universes (u)) as well.

Infinite becomes non-relative, non-local, always a background entity rather than a foreground entity. The constant of 'c' is a horizon constant, and energy and proportionality will be conserved. The plane of the space-verse is a hyper-plane, in fact an infinity of planes (a.k.a. universes (u)). What do I mean by this? The Universe (U) will reset "relativity", make relative to the hyper-plane any momentum, any acceleration in velocity, in the open system. Relativity will lessen and be lost, will breakdown, and be gained or built up as a transition between planes of the hyper-plane. A traveler will be lost to one universe (u) and gained to another universe (u) without ever measuring the speed of light anything other than 186,000 miles per second within its own rest frame of universe (u) local to its self-powering conveyance (thus constant of acceleration). It will go somewhere in an open system (a.k.a. an opening system) and that somewhere will never be the speed of light.

** I erred in identifying Georg Cantor as a famous physicist of his era. He was a noted mathematician of the period. I corrected the above to give him his proper place and due. **
 
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quote "Infinity is a concept. It's not a value that can be acted upon in mathematics ".......in my humble opinion as a non scientist, I find this discussion too unrealistic. How can infinity be a concept ? If I sat in a spaceship, and flew for an (obviously impossible for a human ) amount of time in one direction , I would get to the edge of this universe (ignore its expansion), and could continue in that direction forever; so how can it be a concept when its a physical fact. I also read somewhere that a space/distance could be infinitely small; which although I can understand faraway distance to infinity (never ending), it really puzzles me to consider infinity down to its smallest point, which I would think has a such a small figure that its zero, and how can you have less than zero at a point ..... ?
 

Wolfshadw

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In the simplest way I can put it.

1 + 1 = 2
When you add 1, the original value is changed

Infinity + 1 = Infinity
When you add 1, the original value is not changed. This is not possible, so "infinity" is a "concept" that cannot be acted upon in mathematics.

If there is an edge to the universe, it's not infinite. If the universe is a finite structure, there is no way of knowing whether or not you are able to travel beyond the bounds of the universe. If you were able to travel beyond the edge of the universe, you would still have a starting point. Mathematically, that would be zero. Each mile you travel, you're adding "1".

-Wolf sends
 
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quote "Infinity is a concept. It's not a value that can be acted upon in mathematics ".......in my humble opinion as a non scientist, I find this discussion too unrealistic. How can infinity be a concept ? If I sat in a spaceship, and flew for an (obviously impossible for a human ) amount of time in one direction , I would get to the edge of this universe (ignore its expansion), and could continue in that direction forever; so how can it be a concept when its a physical fact. I also read somewhere that a space/distance could be infinitely small; which although I can understand faraway distance to infinity (never ending), it really puzzles me to consider infinity down to its smallest point, which I would think has a such a small figure that its zero, and how can you have less than zero at a point ..... ?
Pretty good. You don't add infinity, so you don't add up to infinity. No matter how large the figure you add, the end result is an enlarged finite and in no way infinite. My conclusion is that the numeric value of infinity is '1', as in infinite Universe (U) (infinite '1', and certainly not infinite '0', '0' being neither finite nor infinite, is horizon constant (('1') ('-1')) the Mirror mirroring Universe unto itself).

Infinitesimal exists only relative to finite (as entity, an infinitesimal as entity can even take the place of a finite in an infinite scheme of things). Remove the local, the foreground relative, the opposed coin of finite, and you get infinite from infinitesimal (the only thing greater than infinitesimal is infinite: The only thing lesser than infinite is infinitesimal). Infinitesimal ceases to exist separate from infinite. What takes its place (as mathematician Georg Cantor logically put it) is 'proportionality'; including, regarding the universes (u) of the Multiverse at large, e = mc-squared (proactive: e = mc-squaring (an expansive universe?)).

The observable universe exists no where else but in light's holography. It is nothing but a hologram. Even in thinking about that universe, you have to divide it up into innumerable time-verses, which if you provide each with space to go with its time will not match up smoothly space-wise, or rather space-time-wise, with it. If real, the reality must be a segmented -- segmenting -- vortex. A universe frozen in time thirteen billion light years from Earth, can't have stayed frozen in time for thirteen billion years. And there is no way its space and time associates with a space and time universe of ten billion light years from Earth, far less a space and time universe one-billion light years from Earth. Change, if only change, doesn't accelerate as fast coming toward Earth as from Earth expanding out to space and time thirteen billion x 6 trillion miles from Earth; a distant space and time you might as well consider to be thirteen billion years in the future regarding Earth. A 'future' road, regarding time travel, any traveler would have to travel to get that far in space from here. To any life there, Earth, here, Earth's whole universe, is in the distant shadow of the BB.

Would either universe at either end, in fact, be one and the same universe as / with the other's universe? Probably not, the entity of uncertainty, exactly the same as the principle of uncertainty, will have taken full hold between the two and the breakdown of relativity between the two universes would be complete. They might as well be an infinite distance apart; and Multiverse-wise, many universe-wise (cells divided and dividing), could actually be an infinite distance apart, whether plane of velocity deep or point of position broad, or both, no traveler could ever know: or know his way home.

The Universe always dividing into itself will always equal '1', my number equating to infinity (open systemic (including, opening system)). And having worked with computers since the days of systems taking up whole warehouse rooms down to today when I have far more than the same bulk capacity in my laptop (more: no network of any kind, no cloud computing, no virtual cyberspace, existed back then), I know how going small can go large indeed. In other words, cosmologically, to go infinitesimal in place in order to go, at once, infinite in extent. An infinity of finites, such as an infinity of finite universes, is, or can be, at once an infinity of infinitesimals. No more than finite recognizes the existence of infinite, does infinite recognize the existence of finite.

You cannot add any number to the principle of growing uncertainty. Growing uncertainty is what a universe traveler would face. In Chaos Theory there is an entity called a "strange attractor of chaos", and the Multiverse is certainly that, big time. As a matter of fact a continuous adding of numbers regarding mathematics unlimitedly, or in anything else unlimitedly, simply plays to nothing but growing uncertainty and growing chaos. Captain Kirk of the spaceship Enterprise would tell you, though, what n terrifically awesome frontier that would be for any frontiersman or woman.... and mathematics be damned! He would put it like Admiral Farragut once put it in a different regard -- "Damn the torpedoes! Full speed ahead!" Infinity, the unlimited, the potential of the unlimited, is precisely what any true frontiersman or woman dreams of and so many have died reaching out for (and will always risk dying for).
 
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In the simplest way I can put it.

1 + 1 = 2
When you add 1, the original value is changed

Infinity + 1 = Infinity
When you add 1, the original value is not changed. This is not possible, so "infinity" is a "concept" that cannot be acted upon in mathematics.

If there is an edge to the universe, it's not infinite. If the universe is a finite structure, there is no way of knowing whether or not you are able to travel beyond the bounds of the universe. If you were able to travel beyond the edge of the universe, you would still have a starting point. Mathematically, that would be zero. Each mile you travel, you're adding "1".

-Wolf sends
In the simplest way I can put it.

1 + 1 = 2
When you add 1, the original value is changed

Infinity + 1 = Infinity
When you add 1, the original value is not changed. This is not possible, so "infinity" is a "concept" that cannot be acted upon in mathematics.

If there is an edge to the universe, it's not infinite. If the universe is a finite structure, there is no way of knowing whether or not you are able to travel beyond the bounds of the universe. If you were able to travel beyond the edge of the universe, you would still have a starting point. Mathematically, that would be zero. Each mile you travel, you're adding "1".

-Wolf sends
Thanks for the reply wolf, but I'm afraid you are going to have to go even simpler........going beyond the edge of the universe there has to be something. If the BB happened, that matter is expanding outwards (travelling through space) and the space its travelling through, never ever ends . At this point I try to imagine that , and cannot. You mention " if you were able to travel beyond the edge", at which point I am very confused. Trying to picture the nothiness beyond ths universe going on and on and never ever ending is mindblowing. Scientist use complicated unfathomable (to us lay people) maths that is far beyond our comprehension. Simply put, if the universe is an expaning balloon, whats outside the balloon, and infinity indicates there are infinite balloons, and when eventually the ballon{s] deflates or bursts, what happens to all the material of galaxies........
kind rgds
 

Catastrophe

The devil is in the detail
Infinity is not a number.
Infinity = Infinity + 1 = Infinity + 2 = Infinity + Infinity

Take Infinity + 1 = Infinity + 2

Subtract infinity from both sides.

Then 1 = 2

Infinity is not a number. QED.

Cat :)
 
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Thanks for above "Infinity is not a number." Which does not help me at all.
At this point, I , and my questions regarding whats beyond this universe
will not post anymore, because none of the responses assist me with infinity.
But thanks to all, and I hope your discoveries help us all to try and understand
this wonderful universe.
kind rgds
 

Catastrophe

The devil is in the detail
Thanks for above "Infinity is not a number." Which does not help me at all.
At this point, I , and my questions regarding whats beyond this universe
will not post anymore, because none of the responses assist me with infinity.
But thanks to all, and I hope your discoveries help us all to try and understand
this wonderful universe.
kind rgds
Goodbye. Best wishes, Cat :) :) :)
 
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Hang tough to your views, greenrivet. They don't understand what the great historians and others have always understood about shrinking and closing down Old Worlds and revealing great expansionary New World Frontiers beyond to open up and [[in-turn]] shrink and close up, thus to go forever, probably, from old world frontier to New World Frontier. Stephen Hawking called it a potentially ever constant migration of life forward, upward, in space but backward, downward, in time. It's a seemingly static finite geometry but infinity of breadth and depth is the key must element that keeps it forever.

It doesn't add. It opens when closing, building up, revealing, a new always seemingly bigger and better relativity when breaking down the old relativity, leaving behind the old relativity, itself once upon a time considered unlimited in potential.

It doesn't add. It travels to any of an infinity of universes (as Godel put it, "an infinity of infinities") up and/or out, infinitely broad and/or deep, but always stays dead center point-position regarding the constant '0' of horizon. You can travel it, you do in just moving point to point, universe to universe, but you can never observe it for what it is. And if you think I'm just talking infinitesimal point universes, think again, I'm also talking Multiverse's "paralleling universes" in depth. More than one universe in one place (we even joke about it -- "What universe are you from?"). More than one potential in one place. More than one path in one place. Quantum Mechanics, for just one brand of physics, speaks to such deep duality and/or deepening multiplicity of dimensionality in any one place. Infinity doesn't add, no more than an open system, as opposed to a closed system, adds. No more than an opening system, as opposed to a closing system (the one always revealing the other), adds. Infinity and finite are equals. They co-exist. They can even overlay each other.
 
If our BB is all that exists then infinity is what our BB area is.
If our BB is just 1 soap bubble in a sea of soap bubbles then each one is infinity since outside each bubble doesn't have meaning and you can't escape a soap bubble.
Infinity can be just infinity or an endless selection of infinities.
All depends on reality of the universe but infinity will always be infinity even if it's just local infinity.

I tend to think of infinity as soap bubbles that interact in every way possible from bounce to merge to cannibalism .
Probably why we have BB's in the first place is an energy exchange of that process.

JMO
 
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Catastrophe

The devil is in the detail
It all comes down to semantics
IF The Universe is all that there is, then there can only be one.
IF you talk about universes, then you are not talking about The Universe.
No sense will be made in any such discussion until meanings are agreed.

"Your universe is not my Universe"
"No, your Universe is not my universe! until the cows coms home.

If anyone wishes to converse with others, they must share common terms.

Cat :)
 
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It all comes down to semantics
IF The Universe is all that there is, then there can only be one.
IF you talk about universes, then you are not talking about The Universe.
No sense will be made in any such discussion until meanings are agreed.

"Your universe is not my Universe"
"No, your Universe is not my universe! until the cows coms home.

If anyone wishes to converse with others, they must share common terms.

Cat :)
Yep all comes down to what is the universe.
Outside whatever it is doesn't exist unless it is forever then outside never existed.

A local infinity is possible though in a grander set of infinite bb universes.
Still really infinity only as the larger set though and local infinity of a smaller scale.
And if it's smaller then it really isn't infinity.

As you say the (universe) is all.
Until we can prove our thinking of a universe is wrong then more than it isn't a valid question. :)
 
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Suppose infinity doesn't exist, voids don't exist, and that distance is something that can only exist where energy exists. Energy apparently creates space-time in a variety of ways to remain active. We know of two of them - the pre-Big Bang and the aftermath of it.
 
Suppose infinity doesn't exist, voids don't exist, and that distance is something that can only exist where energy exists. Energy apparently creates space-time in a variety of ways to remain active. We know of two of them - the pre-Big Bang and the aftermath of it.
Very possible that distance is just a perspective error.
If (nothing) can exist in the universe because a smallest thing exists then what is distance other that location of something to something.

If we are just one BB area then what is relative if we are already at C or so close to it that time and space are just artifacts of that?

Tough to pinpoint what distance is in a BB area that has no yardstick and lots of fill as nothing between something.

Maybe someday we will discover another neighbor BB area and have some decent guess at relative speeds and what that means for our BB area in the grand scheme of space and time if it exists.
That would be rethink what the universe is day :)
 
It is generally accepted (at least by mathematicians) that there are different infinities countable, uncountable and perhaps more (I’m not an expert in transfinite arithmetic).
https://www.bbvaopenmind.com/en/science/mathematics/georg-cantor-the-man-who-discovered-different-infinities/
https://en.wikipedia.org/wiki/Cantor's_paradox
Needs a rethink of what infinity is and what the universe is IMO.
Infinity after all is forever so whatever part of that isn't infinity or the universe.

For all realistic purpose though our BB area is infinity, just the question of is it all or is it not all.
 
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Needs a rethink of what infinity is and what the universe is IMO.
Infinity after all is forever so whatever part of that isn't infinity or the universe.

For all realistic purpose though our BB area is infinity, just the question of is it all or is it not all.
If it is forever that distant and collapsed constant horizon of infinity, the BB/Planck horizon to an infinity of universes wide and deep, there doesn't have to be a before to it, and/or any other side to it. An endless beginning to go with all those beginningless ends called blackholes. A traveler could travel forever toward it and never get closer to it than when he started out. The radius of the distance is the BB/Planck horizon at one end, and either the traveler at the other end, or any of countless blackholes.

So, what is the thickness of the wall of points to just this side of the BB/Planck horizon? Infinity. You can measure past it radially, but you can never measure to it. You can observe that it is the horizon, but it is a teaser that will always beckon but only put a constant of 'fountain of youth' and evolution between you and itself. Every step in your travel will be a step into the dead middle between horizon(s), even if your steps are to infinity and forever. Horizon to horizon, boundarylessness to boundarylessness, universe to universe (Multiverse), of the Universe.

Why need anything before, or outside, when you find that you are before and outside that horizon? When you finally realize you are inside that horizon and was never anywhere else... will never be anywhere else? Thanks to the Multiverse part (herein the duality of Big Crunch Vortex / Big Hole (Void) Vacuum), as the traveler you just never felt, and never would feel, the hot heat of a 1.420 nonillion degree furnace temperature. The one way wormholes of every blackhole beginningless end that ever was, is, and ever will be, all at once (infinity/forever), point to such a crunch (vortex), at once hole (void) (vacuum).... such an endless beginning at/in BB/Planck horizon. Between the two horizon constants -- inpouring to infinity and outpouring to infinity, the lot of everything else.
 
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