## Does infinity exist?

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### Does infinity exist?

Infinity has a habit of eternally popping up in debates, so I figured I'd put together a thread that is easily referenced upon such occurrence that will dissuade folks from religiously promulgating the concept of infinity as an explanation for the unexplainable.

First, what is it?

infinite
[in-fuh-nit]

1. immeasurably great.
2. indefinitely or exceedingly great.
3. unlimited or unmeasurable in extent of space, duration of time, etc.
4. unbounded or unlimited; boundless; endless.
5. Mathematics: not finite. (of a set) having elements that can be put into one-to-one correspondence with a subset that is not the given set.

Origin of infinite
1350–1400; Middle English < Latin infīnītus boundless.

According to definition #1, there is a sense in which the infinite can describe merely what is not measurable, so in that light, finite amounts can be so large that they are not measurable, yet are still finite. This is not the sense that I intend to deal with when talking about infinity. Finite numbers that are so large that they couldn't be represented on the entirety of the observable universe, even if written on the planck scale, I'm defining those as "dark numbers" because they are finite, but unrepresentable (dark/unseen) within the universe.

Hopefully we can all agree that a good working definition of infinity is "boundless", "without bounds or constraints: either physical or conceptual".

Now, can the boundless exist? Well, what does it mean to exist? This dot exists ---> . because there is something that is not-dot providing contrast and context (the white background), so existence is the relationship of the dot to the not-dot because if either are missing, then there is no dot and no dot could be said to exist. Existence is therefore dependent upon relationship and relationship precedes concepts of existence.

Now, what if the dot had no boundary? Well, immediately we can surmise that it would have no contrast because if the dot had no boundary, there would be nothing that is not-dot to provide the contrast in order to underpin existence. And if there were something to provide contrast, then obviously the dot would have a boundary. So right off the bat we can say infinity isn't anything that can exist, but I'm just getting started.

Infinities are said to contain things, because they contain infinite things, but how can a container contain anything with no walls (boundaries)?

Infinities cannot have beginnings or ends because those are boundaries and we said in the beginning that infinity has no boundaries. We cannot divide infinity in half and say infinity is bounded by this finite location and extends to infinity in that direction; it's nonsense and breaks our definition of infinity being boundless. Zero is not a boundary, but is just an arbitrary starting point on an infinite number line extending in both directions and we could just as easily started at -2,-1,0,1,2,3,etc or 5,6,7,8,etc. A line that is not infinite is a segment because all lines are defined to be infinite within the construct of mathematics; therefore a line with a beginning (such as a timeline) is not an example of infinity. Further, if time had a beginning, infinite time could not be said to exist until forever arrived, and forever means never because forever can never be realized, so infinite time could never exist if time had a beginning.

A better conceptualization for eternity is absence of time instead of infinite amounts of it, but really they both mean the same thing since in both cases time would have no relevance.

Since infinity has no starting point/reference point/unique edge, then infinite computer memory would equate to having no memory and anything written to memory could never be found again. Where would allocation start? Afterall, the memory stick would take every bit of space in the entire universe because to say it wouldn't would be to limit the size of it. Where would an origin/center be placed and how could it be found again?

The infinite is the ubiquitous, omnipresence. If there were infinite oranges, then oranges would exist everywhere there is a place for an orange to exist which would leave no room for anything that is not-orange, and so by having an infinite amount of oranges, we have a non-existence of oranges since there is nothing that is not-orange to provide the contrast and underpin existence. Therefore, what is infinite is nothing and nothing is the only thing there can be infinite amounts of.

Infinity and zero are tied at the hip and every number has a pair: 1-1, 2-2, 3-3, etc. Every number has a negative partner, except zero, but the partner to zero is infinity and, conveniently, neither exist.

Here's more reading on the topic http://theorangeduck.com/page/infinity-doesnt-exist

Here's a debate involving N.J. Wildberger (Yale Phd in Mathematics and former instructor at Stanford and author with extensive youtube channel devoted to math):

Here is a video going into more detail about dark numbers:

Here are a couple youtube comments that resonated well with my sentiments:

Daniel Șuteu

This is like preaching atheism to mathematicians; I imagine in the future that mathematics will become a substitute for religions and religious discussions about the existence of a god will be replaced with discussions about the existence of very large numbers, like our z or its prime factors. I agree with you up to some extent only, and as I'm trying to agree more with you, something inside of me tells me that this does not feel right. The idea of continuity and the consistence of mathematics is quite contradictory with the belief that this rules does actually break up eventually. From a mathematician point of view, the universe is truly infinite in every regard. The limits are imposed by our finite reality, which I think it's only a projection of the true "reality". Nevertheless, understanding the limits of our projected reality can be something useful, as we all live inside it, an d it may give us more clues about the true reality that may or may not exist out there.﻿

njwildberger

Your last phrase sums it up well: "the true reality that may or may not exist out there". Is this the kind of reality we want to consider? How about the reality around us, that we are sure exists, because we have direct evidence for it? How about the reality that our computers reveal?

I am preaching science rather than atheism, via an orientation based on clear definitions, explicit examples and concrete computations. I propose that we move towards a scientific approach to mathematics, not a religious one. Let's replace the abstract study of notions of what might be, with explicit investigations of what is actually here.﻿

Belief in infinity is a religion, because there is no evidence for it and it must be assumed to exist on faith, and there is no arguing with religion.

If anyone has evidence that infinity exists, please post it below. Questions are encouraged, but dogma is not.
Serendipper
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### Re: Does infinity exist?

Trying to be undogmatic, my initial reaction is, that the question is posed in a either/or type looking for answers, and this look degrades in accordance with expanding the point you mention, both temporally, spacially hence conceptuality of the matter under discussion.
This kind of conceptualization began in the middle ages, in an age of doubt, hence cogito ergo sum, the identity of such a construct beginning to form by a binary intellectual process.

Down the line , the cogito changed into esse est percipii, and that reduced the concept of beginning the quest for infinity away from the intellectual doubt toward a search for relative certainty starting with Leibnitz.

The infinite got integrated within the search for it, the perception could be envisioned either as compelled to extend the physical largesse of cosmological bodies even if approaching further and further optical limits, via the limits, including more and more sophisticated radiotelescopic limits.

The farther extended things are out there, the smaller they appear, and the perception of them are sharply reduced to minimum, before they return the question to a bounded nothingness.

Now here is the connection to the ontological , the one to which a scholastic reference is returned. There must be some thing beyond the limit of perception, beyond the horizon,as the lack of perception sets the limit.

This idea corresponds to the way the earth was said to be flat before it became spherical for the conceptual understanding to catch up.

And that is what supports the search into infinity of the large within the inner search with the very small.

The very small compose that which the very large boundaries view as dark matter, and this search has come up with the idea that it is pure energy, but so far having both material and energy characteristics.

The photon has both and this manifests the experience the inquiry can change the very state of whats is inquired.

If perception and its derivative, organic life is a bound to its very development, which is the idea that without perception of something there can not arise an existence beyond the perception of it ; (for that is the basic idea of 'esse est percipii ) then the search for boundaries contains this idea, and then it defines the mathematical limitations differentiating it, in terms of integrating these manifestation into a single concept<infinity>.

Why must there be something beyond the limit of a boundary to suggest that the boundary itself is an artificial construct to uphold the mathematical description of it?

If a limitless boundary is defined as something else other than the content of it, beyond which there must be a nothingness which cannot be perceived, a better way of thinking of limits and boundaries could be would be into visualize the (universe)'es as falling systems which are always self contained, and the boundaries or sets become merely conventional ways of differentiating the cogito from the percipii.

But since the cogito has another boundary the percipii as a conditional requirement for 'existence' which is nothing else but a periphery of a more underlying construct- being, these two realms need to survive in the mode of
how the bounded intellect must be linked to its appreception, the modus operans becomes the glue, for some its god, for some its an eternal return, visualized by a spatial-temporal reintegration for ever, where such a vision again begs on the argument of eternal as another infinite set.

The ultimate question is: Can immeasurability limited, become the understood test for changing- , not cutting away the scholastic notoion that the finite be always the modus operans in defining the degree of overlap between how infinite and finite sets define their content?

Or, are we to talk of certainty as its primal cause of manifestation, then such musings revert to either this or that, and it falls apart.

But if we let the whole idea of excluding sets include into the opposing idea, then again as you implied, the relationships of the bounded dark matter become its conditional existence, in it's self , as to be able to be it'self.

The most that can be said is that the idea of infinity has to include within the specific bounded self, in order to exist. That idea is the product of the percipii, which also needs to be included in the idea of the Cogito, where that is the idea of a higher power.
Last edited by Meno_ on Thu Oct 11, 2018 5:24 pm, edited 1 time in total.
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### Re: Does infinity exist?

If you know, that is can prove via deduction, that infinity does not exist - which for all I know it does not - then you can prove that the universe had a beginning. It has not been here forever. This means Serendipper that you know what astrophysicists have yet to form consensus around. There might be a Nobel in this for you if you shopped your proof around the right observatories.
Karpel Tunnel
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### Re: Does infinity exist?

Yeah I agree with the definition of infinite, though some problem occurred afterwards;

"This dot exists ---> . because there is something that is not-dot providing contrast and context (the white background)"

It would also exist if the screen was filled with black but it wouldn't be visible to a human, only to the computer.
Theres a subtle difference between something that exists and something that has the power to be perceived.
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### Re: Does infinity exist?

So you can say if something has the power to be perceived and is suddenly perceived it loses part of his potential in exchange for an actualization.
When it is being perceived it changes things and this means it also changes unless it is gold. I suppose the potential Time goes between something so fragile it cant even be perceived lest it disintegrates (like a human ) and gold, at the end of the cycle which cant even rust.
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### Re: Does infinity exist?

Oh yeah if time is limited for a Big Bang then time just speeds up or slow down however you see it in any asymptote and still is efficiently eternal, because it is all relative to the next moment. Like the turtle and the hare.
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barbarianhorde
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### Re: Does infinity exist?

Wait what if the Big Bang is like a reversed "Sonic Boom" of light speed. So what is that, Auric Boom.
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barbarianhorde
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### Re: Does infinity exist?

Meno_ wrote:Trying to be undogmatic, my initial reaction is, that the question is posed in a either/or type looking for answers, and this look degrades in accordance with expanding the point you mention, both temporally, spacially hence conceptuality of the matter under discussion.

Well I am open to having my mind changed, but I wasn't planning on it lol. I considered the title as an assertion "Infinity doesn't exist", but decided to not be overly presumptuous and instead phrase it as a question to be answered.

Now here is the connection to the ontological , the one to which a scholastic reference is returned. There must be some thing beyond the limit of perception, beyond the horizon,as the lack of perception sets the limit.

The thing is though, relationship doesn't end with perception. There is still a connection and underpinning relationship even if it isn't physically viewable.

What exists isn't just what we can see, but what is able to relate to something else that exists. For instance the sun could give no light if no planets were around and the photons couldn't even begin their journey unless a destination is already known, so if there is nothing for light to shine on, then there is no light in existence. Relationship underpins existence and that's deeper than just perception. But deeper still is the realization that the relationship actually joins the things together into one thing: there are no planets and sun, but planet-sun relationships.

The photon has both and this manifests the experience the inquiry can change the very state of whats is inquired.

Changing what you're looking at by looking alludes to self-inspection, doesn't it?

Why must there be something beyond the limit of a boundary to suggest that the boundary itself is an artificial construct to uphold the mathematical description of it?

Well, I suppose because things can't be bounded by nothing because there is nothing in nothing to be a boundary.

But that presents a problem since if all things have boundaries and nothingness cannot itself be a boundary, then there must either be infinite things or the one big thing must be infinite in size and both conclusions are unacceptable to me. Instead, I see the problem as a hint to the solution of self-inspection: the thing doing the looking can't also be the thing being observed and if it tries, infinity results like a camera pointed at its own monitor results in infinite regression due to self-inspection. We can't look beyond the boundary simply because what's beyond the boundary is what's doing the looking.

If a limitless boundary is defined as something else other than the content of it, beyond which there must be a nothingness which cannot be perceived, a better way of thinking of limits and boundaries could be would be into visualize the (universe)'es as falling systems which are always self contained, and the boundaries or sets become merely conventional ways of differentiating the cogito from the percipii.

I don't perceive much differentiation between cogito and percipii and was delighted when I found that Goethe didn't either (as if that meant something )

"Thinking… is no more and no less an organ of perception than the eye or ear. Just as the eye perceives colours and the ear sounds, so thinking perceives ideas."

The ultimate question is: Can immeasurability limited, become the understood test for changing- , not cutting away the scholastic notoion that the finite be always the modus operans in defining the degree of overlap between how infinite and finite sets define their content?

This question is hard for me to understand. Can you rephrase it?

But if we let the whole idea of excluding sets include into the opposing idea, then again as you implied, the relationships of the bounded dark matter become its conditional existence, in it's self , as to be able to be it'self.

Yes because things are defined by what they are not. If there is nothing a thing is not, then a thing doesn't exist.

The most that can be said is that the idea of infinity has to include within the specific bounded self, in order to exist.

Again, that seems like self-inspection to me.

Good comments! I appreciate you taking the time
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### Re: Does infinity exist?

Karpel Tunnel wrote:If you know, that is can prove via deduction, that infinity does not exist - which for all I know it does not - then you can prove that the universe had a beginning. It has not been here forever. This means Serendipper that you know what astrophysicists have yet to form consensus around. There might be a Nobel in this for you if you shopped your proof around the right observatories.

I thought we already knew the universe had a beginning. If the universe were infinitely old, then it would have been at thermal equilibrium an eternity ago lol

It just doesn't make any sense to me to think an eternity has passed... gone... forever has come and gone... and here I am after all that time. And then I'll go away for another eternity. That just seems like obvious nonsense to me, but it's so obvious that's it's hard to explain.

This is ultimately why I believe infinity should not be an axiom of mathematics. It cannot be imagined - and it is not right to declare something exists which cannot be imaginable - not even in mathematics. If you say you believe in infinity, say you understand it, say you can manipulate it and do mathematics with it - it isn't true. It can't be imagined, it can't be realized, it can't be used in mathematics - only finite approximations can. You cannot imagine infinity, use infinity, describe, or realize infinity. If you could - it would be finite. Not only does infinity not exist - I think it cannot exist - not in the real world - not in imagination - not in mathematics. http://theorangeduck.com/page/infinity-doesnt-exist
Serendipper
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### Re: Does infinity exist?

barbarianhorde wrote:Yeah I agree with the definition of infinite, though some problem occurred afterwards;

"This dot exists ---> . because there is something that is not-dot providing contrast and context (the white background)"

It would also exist if the screen was filled with black but it wouldn't be visible to a human, only to the computer.
Theres a subtle difference between something that exists and something that has the power to be perceived.

If the computer knows it's there, then the computer has contrasted it from everything else. Essentially you would have told the computer to focus on one coordinate on a black screen and call it a dot, so the computer knows (x,y) because it knows (not-x,not-y).

But give the computer infinite space and there is no (x,y) because there is no edge.
Serendipper
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### Re: Does infinity exist?

barbarianhorde wrote:So you can say if something has the power to be perceived and is suddenly perceived it loses part of his potential in exchange for an actualization.
When it is being perceived it changes things and this means it also changes unless it is gold. I suppose the potential Time goes between something so fragile it cant even be perceived lest it disintegrates (like a human ) and gold, at the end of the cycle which cant even rust.

Gold should decay. Everything is losing energy through electromagnetic radiation (thermal radiation) above absolute zero and at absolute zero there is an identity crisis where nothing has any differentiation from anything else.

Start at 27:00

Here's an electron microscopic view of gold atoms being pulled apart:

Some atoms on the edge seem fuzzy and seem to pop in and out of existence.
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### Re: Does infinity exist?

barbarianhorde wrote:Oh yeah if time is limited for a Big Bang then time just speeds up or slow down however you see it in any asymptote and still is efficiently eternal, because it is all relative to the next moment. Like the turtle and the hare.

Yeah how long is a moment lol. Time isn't a thing, but is an attribute of a thing. d=rt. t=d/r so time is the relationship between distance and velocity.
Serendipper
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### Re: Does infinity exist?

barbarianhorde wrote:Wait what if the Big Bang is like a reversed "Sonic Boom" of light speed. So what is that, Auric Boom.

A sonic boom results from traveling faster than sound can propagate through the medium of air, so an auric boom (cool name btw) would be traveling faster than light can travel through its medium. My next thread is going to be about either the ether through which light travels or the variable speed of light.

A document reported to be of Tesla, but not confirmed, says "The stars, planets and all the universe appeared from the ether when some part of it, due to certain reasons, became less dense. It can be compared with formation of blebs in boiling water although such a comparison is only rough. The ether tries to return itself to its initial state by compressing our world, but intrinsic electric charge within material the world substance obstructs this. It is similar to that when the water compresses blebs filled with hot water steam. Until the steam does get cold the water is unable to compress the bleb. With time, having lost the intrinsic electric charge, our world will be compressed with the ether and is going to turn into ether. Having come out of the ether once - so it will go back into the ether. "

A change in density seems consistent with an auric boom. Anyway, I'll have to start the other thread before I let too many cats out of the bag.
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### Re: Does infinity exist?

A lot of people think this but there is no consensus amongst astrophysicists. I spent an hour at a recent party picking the brain of one. Yes, there was a big expansion, the Big Bang, that has consensus. But was this part of a cycle? Does this happen in the context of a larger metauniverse? and there are other scenarios banded about.
If the universe were infinitely old, then it would have been at thermal equilibrium an eternity ago lol
Nope. I mean, look for a moment at the Big Bang. Suddenly we have all sorts of thermal disequilibrium out of nothing. If that can happen once, for all we know it can happen many times.

It just doesn't make any sense to me to think an eternity has passed... gone... forever has come and gone... and here I am after all that time. And then I'll go away for another eternity. That just seems like obvious nonsense to me, but it's so obvious that's it's hard to explain.
Hey, look, I have similar intuitions. But that and a couple of bucks'll get you a cup of coffee.

At least with my intuitions ALL THE OPTIONS seem absurd. You bring up the second law...that suddenly there appears out of nothing a really wound up clock that will for a while than stop. That seems ridiculous. That the universe is finite with neither nothing nor something outside it. That seems ridiculous. That the universe isn't more simple, instead of say a single dense cube, seems ridiculous to me. The results of the double slit experiments, relativity, both seem ridiculous to me. And more....
Karpel Tunnel
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### Re: Does infinity exist?

Yeah a sonic boom is when the sound that normally would go ahead of the object (say a noisy craft) gets caught up by the craft and joins the sound the craft leaves behind.

It is very simple logic I did when I was 6 proving there is no beginning. But my Auric Boom concept which im just working on now maybe can explain that there is a bottom of what can be perceived.
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### Re: Does infinity exist?

Serendipper wrote:Hopefully we can all agree that a good working definition of infinity is "boundless", "without bounds or constraints: either physical or conceptual".

I'm afraid I must dash your hope. To the extent that I may personally be included in the "we" of your claim; I do NOT agree that "a good working definition of infinity is "boundless"".

Even Aristotle noted the point I'm about to make. He noted that there's potential infinity in the upward direction, as in 1, 2, 3, 4, 5, ... And there's potential infinity in the downward direction: 1/2, 1/4, 1/8, etc. Downward infinity has of course both mathematical and physical implications. Mathematically, it says that there is no smallest positive rational number. This led to a couple of thousand year of trying to logically deal with the infinitely small, which mathematicians finally did in the 19th century by way of the theory of limits.

Physically, of course, we have the question of whether matter and indeed spacetime itself may be indefinitely divided; or if to the contrary, we live in a discrete grid. This question is very much open, with passionate adherents on each side.

Having noted the infinitely small, I ask you to consider as a mathematical example the closed unit interval [0,1], which is defined as the set of all real numbers between 0 and 1, inclusive.

We know that this set contains infinitely many real numbers; in fact, an uncountable infinity of them. Yet this set is bounded. Indeed, no element of the set ever gets smaller than 0 or larger than 1. And the set has a boundary, namely the set consisting of 0 and 1. No real number can go past those points.

I submit to you the set [0,1] as a collection of real numbers, or geometrical points if you wish to think of them that way, that is:

* Infinite; and

* Bounded.

In conclusion I note that it's often counterproductive to use dictionary definitions for technical terms. There are plenty of bounded, infinite sets. And if you believe the physical world is continuous, there's infinity in a grain of sand. As William Blake wrote:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

Augeries of Innocence
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### Re: Does infinity exist?

Karpel Tunnel wrote:
A lot of people think this but there is no consensus amongst astrophysicists. I spent an hour at a recent party picking the brain of one. Yes, there was a big expansion, the Big Bang, that has consensus. But was this part of a cycle? Does this happen in the context of a larger metauniverse? and there are other scenarios banded about.

Yes but cycles have beginnings (arbitrary ones).

If the universe were infinitely old, then it would have been at thermal equilibrium an eternity ago lol
Nope. I mean, look for a moment at the Big Bang. Suddenly we have all sorts of thermal disequilibrium out of nothing. If that can happen once, for all we know it can happen many times.

I was referring to a steady state universe that didn't have a genesis. In that case, it would be thermal equilibrium. It's the genesis that causes the disequilibrium that, given infinite time, would cool to equilibrium. So if infinite time were already behind us, the universe would already be cool.

Time was created at the big bang as an artifact/consequence of space or some resistance to traveling through it. What caused the big bang isn't spacially nor temporally confined since we can't have self-causation. The thing that is created can't be the cause for the creation of the thing. There was a T=0 because T was made.

It just doesn't make any sense to me to think an eternity has passed... gone... forever has come and gone... and here I am after all that time. And then I'll go away for another eternity. That just seems like obvious nonsense to me, but it's so obvious that's it's hard to explain.
Hey, look, I have similar intuitions. But that and a couple of bucks'll get you a cup of coffee.

It's the problem of how to explain to the blind man what red looks like. I can see it clearly, but I can't explain what I see. So the nobel prize will have to wait until everyone else develops sense organs lol. Newton and Einstein probably weren't the first to think of their ideas, but they did it in a time that was conducive to acceptance of those ideas. Newton himself said "people aren't ready" and who knows if we know all he knew. Same with Tesla and especially Tesla. It's less about the genius and more about everyone else.

At least with my intuitions ALL THE OPTIONS seem absurd. You bring up the second law...that suddenly there appears out of nothing a really wound up clock that will for a while than stop. That seems ridiculous. That the universe is finite with neither nothing nor something outside it. That seems ridiculous. That the universe isn't more simple, instead of say a single dense cube, seems ridiculous to me. The results of the double slit experiments, relativity, both seem ridiculous to me. And more....

That's a strong hint brother: looking at yourself is absurd.
Serendipper
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### Re: Does infinity exist?

wtf wrote:
Serendipper wrote:Hopefully we can all agree that a good working definition of infinity is "boundless", "without bounds or constraints: either physical or conceptual".

I'm afraid I must dash your hope. To the extent that I may personally be included in the "we" of your claim; I do NOT agree that "a good working definition of infinity is "boundless"".

You should submit a better definition in that case.

Below, you're proceeding to talk about what you haven't defined. What do you mean when you say there are "infinite" numbers between 1 and 0 if infinity is not boundless? The first step in an argument is to define terms clearly before using the terms to construct an argument, otherwise you're saying a+b+c=z but not saying what the variables are. Defining terms commits you to what you're saying.

Even Aristotle noted the point I'm about to make. He noted that there's potential infinity in the upward direction, as in 1, 2, 3, 4, 5,

Probably why 1+2+3+4+5+.... forever = -1/12

"potential" is the key word.

Infinity doesn't exist. If it did, the sum of all natural numbers would certainly equal it.

The sum of all squares = 0

The sum of all cubes = 1/120

Having noted the infinitely small, I ask you to consider as a mathematical example the closed unit interval [0,1], which is defined as the set of all real numbers between 0 and 1, inclusive.

You're making divisions where there are none, or did you forget that you cut it? You're creating differentiations on the fly and will need an infinite amount of time to finish, so you're assuming infinity in your proof of it. This was spelled out nicely in the article I posted http://theorangeduck.com/page/infinity-doesnt-exist

The obvious argument for infinity existing is that, given some number, it is always possible to add one to get a new number. Therefore there must be an infinite number of numbers.

The problem with this argument is that it presupposes infinity exists already. More specifically it assumes that a process can be repeated an infinite number of times. If you can't repeat a process infinitely, and there isn't infinite time, it isn't possible to continue adding one forever.

Likewise, you're just adding new numbers between 0 and 1 and you're reliant upon infinite time to complete the process, but if you stop to inspect along the way, the answer will always be finite.

That is why 1-1+1-1+1-1... forever = 1/2 because if you stop, you get either 0 or 1.

We know that this set contains infinitely many real numbers;

No, you've defined it to be so. You're not observing, but conjuring.

Indeed, no element of the set ever gets smaller than 0 or larger than 1. And the set has a boundary, namely the set consisting of 0 and 1. No real number can go past those points.

You've defined the universe to be a fraction 1/x where x >1, so you've just moved the goal posts from simply counting forever to counting forever and plugging into a function... it's the same problem of using infinity to prove infinity. You need an infinite amount of x to prove there are infinite amounts between 1 and 0. Why bother? Just prove there are infinite x >1.

In conclusion I note that it's often counterproductive to use dictionary definitions for technical terms. There are plenty of bounded, infinite sets. And if you believe the physical world is continuous, there's infinity in a grain of sand. As William Blake wrote:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

He also said "A fool who persists in his folly will become wise."

You can only cut something so many times before the knife becomes larger than the thing you're cutting and that fact will become self-evident once you begin and persist in cutting.

The only way to "have" infinity is to stop the process, but if you stop the process, the result will always be finite.
Serendipper
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### Re: Does infinity exist?

Serendipper wrote:Yes but cycles have beginnings (arbitrary ones).
Sure, but then those cycles could be taking place in an infinite span of time.

I was referring to a steady state universe that didn't have a genesis. In that case, it would be thermal equilibrium. It's the genesis that causes the disequilibrium that, given infinite time, would cool to equilibrium. So if infinite time were already behind us, the universe would already be cool.
Yeah, I got that. But the Big Bang being the begining is predicated on the idea that out of nothing a giant really highly wound up clock is created. IOW energy in a state that can run down and it will take a long time. If that can happen, then an infinite universe going back in time could have this happen over and over. We are already accepting the 'suddenly there is a really well wound up clock running down out of nothing' as a possibility. Well, that little miracle could happen over and over.

Time was created at the big bang as an artifact/consequence of space or some resistance to traveling through it. What caused the big bang isn't spacially nor temporally confined since we can't have self-causation. The thing that is created can't be the cause for the creation of the thing. There was a T=0 because T was made.
Some cosmologists think this is a the case, but there is no consensus. We cannot turn to current astrophysics to dtermine the universe being around for a finite time or not. As I said there are a number of other ideas out there, none of them denying the Big Expansion, but placing it in a longer time frame.

It's the problem of how to explain to the blind man what red looks like. I can see it clearly, but I can't explain what I see. So the nobel prize will have to wait until everyone else develops sense organs lol. Newton and Einstein probably weren't the first to think of their ideas, but they did it in a time that was conducive to acceptance of those ideas. Newton himself said "people aren't ready" and who knows if we know all he knew. Same with Tesla and especially Tesla. It's less about the genius and more about everyone else.
Well, this and two bucks gets me a cup of coffee.

That's a strong hint brother: looking at yourself is absurd.
You seem to be agreeing with my point. That something is obvious to you could have to do with oracular insight or it could have to do with built in biases.
Karpel Tunnel
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### Re: Does infinity exist?

Here is a possible-probable-certainty:::

That observed things , the farther/or nearer they get from a point of view, reach observable limits, where they come upon cosmic or mini black holes, which may symbolize some no d of entry into some other state. These states can begin the process of experiencing other limits, from other vantage points of observation, each removed from particular spatial temporal manifestations.

In this scheme, infinity is always a non discernible point a way from its absolute limit.

The difference is, that this negates the absolute manifestation into relative at
any point, suggesting that perception and cognition changes an underlying absolute into its relational, or, relative aspect.

This is why consciousness is never absolutely cignuscient of its object, because it changes it , in a process of increasing proximal awareness of it.

However it doesent negate the absoluteness of the absoluteness of its being. If it were so, it would destroy the process of the conceptual framework of relativity.

So in this scheme relational existence has to ascertain its absolute being-ness.Or, infinity as an absolute can never overtly and absolutely be realized, because this would undermine its own existential requirement, of necessity.
Meno_
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### Re: Does infinity exist?

..though it can be imagined, infinity can never be reached/achieved, so it doesn't ever get to exist.. poor infinity, huh.
The possibility of anything we can imagine existing is endless and infinite.. - MagsJ
I haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something at some point in time.. Huh! - MagsJ
You’re suggestions and I, just simply don’t mix.. like oil on water, or a really bad DJ - MagsJ

MagsJ
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### Re: Does infinity exist?

Karpel Tunnel wrote:
Serendipper wrote:Yes but cycles have beginnings (arbitrary ones).
Sure, but then those cycles could be taking place in an infinite span of time.

In that case the cycles would be infinitely reoccurring meaning we've already had this conversation an infinite number of times and are destined to have it infinitely more. Don't you remember what I said last time? Why must we keep rehashing this throughout eternity?

It also means we've had this conversation infinite times while wearing pink tutus and sitting in chairs suspended by helium balloons. It means any possible variation has already happened infinite times.

I don't think I'm equipped to really disprove that, and I can't appeal to absurdity, but I just can't accept the notion. Maybe I'm dogmatic

But more to the point and all joking aside, how could cycles take place inside infinite time if time only exists inside the cycle?

The same goes for space: how can we have concepts of space outside space if "outside" is a concept of space?

I was referring to a steady state universe that didn't have a genesis. In that case, it would be thermal equilibrium. It's the genesis that causes the disequilibrium that, given infinite time, would cool to equilibrium. So if infinite time were already behind us, the universe would already be cool.
Yeah, I got that. But the Big Bang being the begining is predicated on the idea that out of nothing a giant really highly wound up clock is created.

Obviously the energy that went into winding the spring is eternal, but that's absence of time instead of infinite amounts of it. Energy doesn't observe time or space, but defines it. Energy travels at the maximum speed, which is instant ( because when you travel c, no time passes, so it's instant).

If that can happen, then an infinite universe going back in time could have this happen over and over. We are already accepting the 'suddenly there is a really well wound up clock running down out of nothing' as a possibility. Well, that little miracle could happen over and over.

What does it mean to happen over and over outside of time and space?

Time was created at the big bang as an artifact/consequence of space or some resistance to traveling through it. What caused the big bang isn't spacially nor temporally confined since we can't have self-causation. The thing that is created can't be the cause for the creation of the thing. There was a T=0 because T was made.
Some cosmologists think this is a the case, but there is no consensus. We cannot turn to current astrophysics to dtermine the universe being around for a finite time or not. As I said there are a number of other ideas out there, none of them denying the Big Expansion, but placing it in a longer time frame.

Time is a relation of one thing to another thing. It takes me 1/24 revolution of the earth to drive 60 miles. We relate time to the decay of atoms or the speed of light, so time is a relation of one thing to another thing and there were no things before the big bang, except the one thing that caused the big bang.

It's the problem of how to explain to the blind man what red looks like. I can see it clearly, but I can't explain what I see. So the nobel prize will have to wait until everyone else develops sense organs lol. Newton and Einstein probably weren't the first to think of their ideas, but they did it in a time that was conducive to acceptance of those ideas. Newton himself said "people aren't ready" and who knows if we know all he knew. Same with Tesla and especially Tesla. It's less about the genius and more about everyone else.
Well, this and two bucks gets me a cup of coffee.

That's a strong hint brother: looking at yourself is absurd.
You seem to be agreeing with my point. That something is obvious to you could have to do with oracular insight or it could have to do with built in biases.

No doubt I have confirmation bias
Serendipper
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### Re: Does infinity exist?

Meno_ wrote:Here is a possible-probable-certainty:::

That observed things , the farther/or nearer they get from a point of view, reach observable limits, where they come upon cosmic or mini black holes, which may symbolize some no d of entry into some other state. These states can begin the process of experiencing other limits, from other vantage points of observation, each removed from particular spatial temporal manifestations.

In this scheme, infinity is always a non discernible point a way from its absolute limit.

The difference is, that this negates the absolute manifestation into relative at
any point, suggesting that perception and cognition changes an underlying absolute into its relational, or, relative aspect.

This is why consciousness is never absolutely cogniscient of its object, because it changes it , in a process of increasing proximal awareness of it.

Right, the thing doing the looking changes the thing by the looking; hence, infinite regression.

However it doesent negate the absoluteness of the absoluteness of its being. If it were so, it would destroy the process of the conceptual framework of relativity.

So in this scheme relational existence has to ascertain its absolute being-ness.Or, infinity as an absolute can never overtly and absolutely be realized, because this would undermine its own existential requirement, of necessity.

It would seem that something must be absolute, but there will never be a way to tell what it is because infinite regression will always result from self-inspection.
Serendipper
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### Re: Does infinity exist?

MagsJ wrote:..though it can be imagined, infinity can never be reached/achieved, so it doesn't ever get to exist.. poor infinity, huh.

Yes that sums up the situation I think.
Serendipper
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### Re: Does infinity exist?

Serendipper wrote:In that case the cycles would be infinitely reoccurring meaning we've already had this conversation an infinite number of times and are destined to have it infinitely more. Don't you remember what I said last time? Why must we keep rehashing this throughout eternity?
Well, right off the bat, there's an infinity. Second, if there is a finite number of possible moments, then it must recycle, if not, not.

It also means we've had this conversation infinite times while wearing pink tutus and sitting in chairs suspended by helium balloons. It means any possible variation has already happened infinite times.
Could be.

But more to the point and all joking aside, how could cycles take place inside infinite time if time only exists inside the cycle?
Well, again, in astrophysics - me going by what I have read, and then also going by me cornering an astrophysicist at a recent gathering - it is not consensus that time started just before the Big Expansion or that there are not other cycles - the same or otherwise - have gone before or that the Big Bang did not take place within a larger universe context. IOW that Big Bang was local. I asked specfically about infinite time and volume and neither have been ruled out and there is no clear majority either.

Obviously the energy that went into winding the spring is eternal, but that's absence of time instead of infinite amounts of it. Energy doesn't observe time or space, but defines it. Energy travels at the maximum speed, which is instant ( because when you travel c, no time passes, so it's instant).
Again, if we allow for there suddenly being an extremely neg-entopic state, we cannot then rule out other hypotheses based on the second law. We allow, in this one version of the Big Bang theory, for the sudden negentropic creation of everything. Once that is one of the axioms of your belief, you cannot criticize other theories for seeming to violate the second law, since you've already done it yourself. Well, it only happened once, it not a great defense.

What does it mean to happen over and over outside of time and space?
Not outside, but as time and space.

Time is a relation of one thing to another thing. It takes me 1/24 revolution of the earth to drive 60 miles. We relate time to the decay of atoms or the speed of light, so time is a relation of one thing to another thing and there were no things before the big bang, except the one thing that caused the big bang.
You can say this, but again, there is no consensus this is the case. And since we do not know what that 'one thing' was, we do not know what it's limits are, if it is still present, if something can reboot or reenergize what is happening nad so on.

No doubt I have confirmation bias
You mean you're actually getting data on this??????
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