Does Infinity exist?
 

I have been having an argument with a mate lately on the matter of defining what exactly infinity is. I believe it is one of the following possibilities:

1) A number so large it cannot be defined.
2) An expression so large it cannot be defined.
3) A term encompassing all space and time (completely devoid of any numeric value).

I believe that answer 3) is the correct. A common example used in our argument is the half-distance paradox. If I walk halfway to point 'A', and half that distance, and half that distance, etc.... I believe I will eventually make it if I take an infinite number of steps. 1/2^n = zero in my books. I reasoned that the only way this is possible is if infinity can be defined as 3).

What do you guys think? Remember to think in 11-dimensional terms...

..

There are larger quantities than infinity.

For example, suppose you had a hotel with an infinite amount of rooms, each room holds one guest. This is big, right?

Wrong.

My hotel has an infinite amount of rooms but each room holds an infinite amount of guests.

If we represent infinity as "N", and call your hotel N1, we can call my hotel N2, to signify the increased holding power.

This is the sort of logic that is needed to construct the quantity that holds all points in space, that is N4.

But yes, infinity, just as zero, exists (at least as a concept).

(If anyone cares to correct this, feel free. I'm digging this up from over 24 years ago.)

i agree with Lebell; it exists because it is a concept.

i dont think infinity can be defined by any numberical terms because it isn't a number.

So you're saying that it exists, but it's not a number... meaning it doesn't exist?

i think infinity exists

i don't think it's a number because you can't place it on a number line....in terms of numbers it could be compared to the square root of -1. you can use it in math, but its not a real number.

i think infinity is simply an idea that exists in our heads, i don't think there is really a way to define it, or there is no definition that would please everyone because it only exists in our minds

While you can conceptualize a difference between N1 and N2, mathmatically there should be no effective difference. You are introducing a new dimension, not a new quantity.

To me, the best way to think of infinity is to plot x^(-1):
try it here:
http://people.hofstra.edu/staff/stev...Graf/Graf.html

Looking at the upper right quadrant, the line NEVER crosses the x-axis. So, Y is positive for x = [0 to +infinity} and y is negative for x= [0 to -infinity}...plug any number into it, and you'll see that this holds. Also, if you double that number, y is still of the same sign.

So, to me, infinity is perpetuity in a particular direciton (either positive or negative from a given starting point). And represents not just one, but all possible numbers in that direction.

#3 can't be correct, because if infinity = all time and space, that still puts a limit on it. Which means if infinity exists there's something outside that.... and outside that.... and--- *dreamer's brain explodes*

Infinity is...erm...spoken of in many ways. Most commonly, I've heard it used as a certain sort of quantity. Any set which is such that it is at least as large as the natural numbers (1, 2, 3, ...) is infinite in size. Lebell is right that there are different sizes of infinity. Georg Cantor proved that the set of real numbers is strictly larger than the set of natural numbers, and also that the power set* of any infinite set is larger than that set. Most mathematicians today hold to the continuum hypothesis, which is that there are no sets of a size between the natural numbers (N), the power set of N, the power set of the power set of N, etc.

*A power set is the set of all subsets of a set. So if my set is {1, 2, 3}, the power set would be {{1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}}

y'all REALLY want your heads blown? some things are MORE infinite than others. :) take some advanced math classes. abstract algebra and up. fun stuff. ;)

Set theory gets into it, although I've never seen exactly what astaris's talking about.

Actually, as far as I can tell, I was saying the same thing as you.

Well there are several ways to define it.
One is a practical way as to get an undeterminate scale for your model,
although this might not be the TRUE infinity, it is still a number too large to count.
This is the definition that I think is relevant for physical purposes.

but on a philosophical or mathematical angle...
The interesting thing is that Lebell said that infinity could represent N1 and another as N2
adding each infinity together N1 + N2 = infinity

But then you could go beyond this to N1 + N2 + N3.....etc.
or N1 * N2 * N3....and so on
or even better
N1 ^ N2 ^ N3...on to infinity.

Interestingly even the concept of infinity has scales.

A good book to read on this is "Infinity & the Mind" by Rudy Rucker

Hmmm...In my math classes infinity was defined as not a number, but more or less as a vector, or direction.

To put it this way, if you have a function that approaches infinity (take a limit of sorts), you will know that as x (or any variable) increases, there will be a proportionality function that is the actual function that describes how the other variable increases.

For example, the function f(x)=1/x, as x approaches 0 from either side, the function f(x) will increase exponentially with each iteration. In that sense, infinity can never be reached because of the computational power of both the human mind or the graphing utility. Therefore, we define infinity to be a dirction to which a function approaches.

Sorry if that made no sense, I just woke up :)

as defined by webster...
 

it's a concept, it exists be cause we say it does, there is no denying that it exists. what it actually is?, is what we are discussing.

infinity isn't a number. numbers are infinite, (they go on forever).
-------------
as defined by webster:

infinity: the quality of being infinite.

infinite:
1:extending indefinitely :ENDLESS <infinite space>
2:immeasurably or inconceivably great or extensive :INEXHAUSTIBLE < infinite patience >
3:subject to no limitation or external determination
4a :extending beyond, lying beyond, or being greater than any preassigned finite value however large < infinite number of positive numbers >
4b:extending to infinity < infinite plane surface >
4c:characterized by an infinite number of elements or terms < an infinite set > < an infinite series >

It exists, but it can't be represented as a NUMBER, however infinity does have a symbol (figure 8).

Meridae'n is displaying some of the most common misconceptions surrounding the phenomenon that is "infinity".

Here is a great article about what it is, but more importantly, what it isn't.

http://www.kuro5hin.org/story/2003/6/3/95744/71866

Infinity most certainly exists.

This question is like asking "Do dreams exist?" Or "Does love exist?"

All have the same answer.

It's just a concept. I believe everything is finite.

hm. how do the concepts of infinity and eternity ... work together/come together, if at all?

Concepts exist only in our minds. Does the number '4' exist?
If there are four apples on a plate . . . the apples are not 'aware' that they are in a group of 4 . . . . the just exist individually. The idea that there are 4 of them is our way of counting them. If we use binary instead of base 10 to count them then there wouldnt be 4 of them (I am sure some clever person on here can tell me what 4 is in binary!).

Whats binary for infinity?

all of this is way over my head mathmatically, but i am very interested in the concept. the idea of "endless" boggles me. i don't like numbers--i just like "endless." and i hope it exists...in a manner of speaking.

I think infinity is going around in patterns/circles of logic, just look at the symbol for infinity. That's all I'm going to say.

Is this where multi dimensions coms in to play?

If the big bang has happend; what is the area that it has not yet expanded to?

Is infinity not just a general term for a number without limit, whereas an eternity is specifically about time.

given that "infinity (is) not just a general term for a number without limit, whereas an eternity is specifically about time", how does space figure in?

I have found infinity! You guys are trying to be all intelligent, when it was out there for someone to find all along!

Picture of Infinity (Link)

symbol for infinity: http://www.wfu.edu/~rbhm/math2/infinity.jpg
(if you have a mac, type option-5)

http://mathforum.org/dr.math/faq/faq.large.numbers.html

http://www.c3.lanl.gov/mega-math/wor...ty/inbkgd.html

http://www.c3.lanl.gov/mega-math/glo.../infinity.html

<hr>

Infinity is not a number or a thing, but the idea behind many notions:

• no matter how high you count, you can always count higher.
• no matter how long you draw a pair of parallel lines, they never meet.
• if you start with a line of any length, you can divide it in half, then divide one of the pieces in half, and no matter how many times you repeat the process, you will always have another piece that you can divide in half again.

Time is not finite.

I delare Shenanagins!
Godel went insane, and so did Cantror trying to prove shit about infinity.
They wavered between the number of points on the real line being, (in their notation, Aleph1 or Aleph(infinity).)
Where Aleph1 = 2^ Aleph0, Aleph2 = Aleph1 ^ Aleph1.

Eventually, Godel through his incompleteness theorem proved that either one could be true because Mathematics is incomplete.

Infinity is not a number, and it doesn't exist. (In this world.)
The world is finite. So there is no infinity.
It's just a concept. Like the point mass.

Binary for 4: 100.
Binary for Infinity ......1111111111111........

If you use binary to count the apples, there are still four of them.
You are just notating it differently. It's just liek saying that if a person in spanish count the apples there are not 4 of then, but quatro. It's just in a different language.

And how do you know that the apples are not aware that there are 4 of them in a room? Can you speak to apples? Can you read apple minds?

Apples dont have minds (except maybe for a Granny Smith) . . . . . . . and even if they did I bet they couldnt count to 4 (or 100 or quatro!) . . my dod had a mind and it couldnt count so I can safely conclude that apples are not numerate. Although one did fall on Newtons head so maybe . . . . . . . . ?

dod! I meant dog

Mathematically, specifically in Calculus, you can never assign a term or variable as 'infinity'. The closest you can say is that as a variable "approaches infinity", here's what happens. You can never reach infinity. Calculus is a pretty narrow construct, though, so this use of infinity can't be universal. Just when integrating.

answers to the following questions:

Does Infinity Exist? Yes it does.
Is infinity a number? No it isn't.
What is infinity? The concept of "endless."

I love your ruthless logic MacGnG!
Would it be ironic if everyone posted to this thread every now and then just to keep it alive to infinity? Or would that just be a sad waste of time and resources . . . ?

1 and 2 can't be correct either then because, based on the way they are worded, infinity would be a single large number or expression which would still be finite. Infinity is a reality which cannot be easily conceptualized. We tend to define our reality based on limits, which makes it difficult defining something that is endless.

can you prove this?

cause i mean logic, we dont need that.

Not just in calculus, but in all algebra. A variable stands for a number, but infinity is not a number.

You can think of it this way:

5/0 = x
Now, if you think it out logically, x becomes infinity. The sameller the denominator gets the larger x gets, so when the denominator is as small as possible, x is as large as possible, hence as the denominator "approaches" zero, x approaches infinity. But we cannot say that x = infinity, instead, x is undefined.
Heres why:
5/0 = x ; x = infinity
6/0 = y ; y = infinity
x=y
therefore 5 = 6.

All numbers are finite. By this I don't mean that there is a finite AMOUNT of numbers, but rather that any particluar number is finite. Hence infity is not a number and you cannot perform artithmetic operations on it.
It is similar in some ways to zero:
X*Z = Y*Z
therefore X=Y
but what if z=0? Well in that case, we can't "cancel" the Zs, as that would be divideing by zero, hence coming up with an undefined term.
In a similar way that algebra and artithmetic seem to work slightly counter-intuitively when zero is concerned, it is the same with infinity, only more-so!
Infinity + Any number still equals infinity! Or is undefined.
Infinity - any number still equals infinitiy or undefined: Inifiny - Infinity = ?
You may straigt away say zero, but think about it. You have infinte marbles, and you take away half of them. You are taking away half of infinity,which is infinity. Hence infinity - infinity = infinity!
Infinity * any number still equals infinity, or undefined: What if we multiply infinity by zero. what is the result? Again undefined!

So, in mathermatics, arithemetic involving infinitiy is very awkward. Infinity is not a number. But does it EXIST?

Well, as already has been stated, it certaintly exists in the world of mathermatics, we have defined, therefore it exists!

But does it exist in the empirical world? Well we certaintly can't MEASURE a length of infinity, even if the universe is infitly big (which I doubt).
Many systems believed to be continous, were proved to be infact quatisised (or discrete) in the 1900s, such as the frequencies of light, and the energies of particles. But if there remains any purely continous system, we can deduce the existence of infinity.
Take for instance space. If you accept that length is a continous dimension and is not discrete, like a computer screen which is made up of discrete pixels.
Take a meter stick. Now somewhere on that meter stick place an imaginary atom. Now move it, and place it some where else? How many possible positions exist for this atom? An infinite number!* Infinity exists.
Now subtract from you meter stick 10cm. Does this change the number of available positions for your atom? No, they are still infinite. What if you break it in two? What if you increase it's length. what if you "square" it? Instead of a one dimensional length, use a square metre area. Still infinity. But surely there are "more" available positions in a whole 1m^2 area than in a 1m length? Well, yes and no...remember that infinity is not a number, and so one infinity is not more than another.

*Two subnotes:
1 The number of positions is not equal to the number of atoms that make up a one meter length. Remember that now that you have placed you atom, you can push it left by half the width of an atom...or a quarter...or an eight...etc.
2 I am aware that an atom does not ocupy a discrete location, I am using it purely as an analogy.

. . . but you cant use the term 'to infinity' without it being relative to the measure of something. eg. saying somethings length extends to infinity . . or saying the time taken extends to infinity. Infinity is the adjective for a measurement for which the upper limit cannot be defined. Infinity is the word we use when we DONT KNOW what the real limit is. Its just like saying "I dont know".

Just replace the word infinity with "I dont know" . . . . .
"So how big is the universe then daddy?" Hmmm (he thinks. Well actually I dont know . . .so I'll just say "its as big as infinity"!


Go on . . try it . . just replace infinity with "I dont know" . . .works every time.

This is absolutely not true. Ininifty is NOT an upper limit. It is not simply a number so large that it cannot be defined.

"x becomes infinity"
NO, THIS CAN NEVER HAPPEN.


x can approach infinity

As a concept, yes, infinity exists. As an actual number, no.

I was trying to say that infinity is the lack of an upper limit. It reflects our inability to calculate an upper limit . . in a similar way that we cannot 'calculate' the meaning of life so we 'invent' god to expalin it all. God = Infinity . . . . . . . . . . both are abstract concepts which neatly explain that which we cannot 'define'.

infinity is without measure on any known scale because math is not complete.

math is not complete . . it should be maths!

Maybe numbers are a huge loop and somehow positives will meet up with negatives again! now that would be crazy hehehe

Re: Does Infinity exist?
 

sounds like an argument i had with a friend of mine a while ago in a math class, infinity does exist, the definitions of it as all-encompassing are totally acurate, there is no boundary, but it's the definition of the concept by humans that consolidates the impossibility of infinity into a useable idea.

HAHA maybe.... but what would it be called?

infinity exists as infinity just like pi exists as pi.

i belive infinity is just the common name used to describe all values greater than or equal to the total number of natural numbers in existance.

So it is defined, but it holds multiple values and not just one particular value.

And i also believe that in mathematics in particular, its not infinity that is important, its how you got to infinity that makes all the difference.

infinity is not a number it's just a way to describe something that is endless (sometyhing that goes on forever).

numbers are endless = numbers are infinite

A lot of incorrect statements about infinity in this thread. In mathematics, there are numbers outside the set of real numbers. Remember that even the integers are conceptual, they're just an easier concept. All the numbers are represented by symbols, so I don't see why the symbol '4' is any different in that sense than the infinity symbol.

There are many mathematic formulas that depend on infinity. There was a guy named George Cantor who proved mathematically that there are different orders of infinity (he named them Aleph 1, Aleph 2, etc). Debating whether infinity exist is not as much like debating whether dreams exist, as it is like debating whether 7 exists.

yes we know infinity exists, we are not debating that; although some people still do not understand that. others do not understand what infinity is, even though we have stated it MANY times and explained it many ways.

Close, except that you simply described N^2 rather than 2^N (where ^ is the power function and N is positive integers). By the axiom of choice we decide that 2^N=R, the real line. To get to R we'd need a list of all the infinitely long hotels (not just an infinite list of infinite hotels). The easiest mathematically correct proof is to extend the Power Function to infinite series, although this is still non-trivial. Heuristically, the power function (in topological terms) is the set of all possible subsets of a set. We know by induction that for any finite set there is no mapping from the set to its power set. {By contradiction} Consider some set (S) and its power set (P). Let A be an onto, 1-1 map from S to P. Consider the set A^-1(P) = S (the reverse mapping from an element of the power set to the original set), then we can simply "swap" orderings such that for each A^-1i (the ith element of the inverse map) matches Pi such that Si = Pi. But this means there is some Pj such that Pj != Sj, because we could simply consider the element Aj = Pj = (Si,Sk), Si!=Sk. This means that there is no onto, 1-1 function from S to P, which means that |S|<|P|, where |*| is the "size of" operations. Trivially we can map Pj->Sj, for Pj = {Sj} for an onto, 1-1 map, meaning that |S|!>|P|, thus |P|>|S|.

This obviously has flaws, but you get the idea.

Yes, the complete integers are a field defined over addition and multiplication. They are the infinite extension of finite rings and fields, for example, {1,2,3} under the operator ^, where 1^1=2, 2^1=3, 3^1=1.

Sorry for the double post. :D

as I understand, infinity may not be an upper limit, but it is equal to a Frank (which was an old way of one upmanship, where "I know the biggest number!" and then youd tell them a frank is bigger, where a frank is your number + 1)

so by such logic, infinity = frank(infinity)

On a number line, infinity can be placed. See the arrow at the end there? thats infinity, at least as far as I can tell, nothing gets much bigger than that arrow.

On the mathematical side of proofs, I have nothing, but its really just the concept that seems to matter.

Yeah, infinity exists as a concept, but not as an actual number, for instance when you think oh, 'infinity + 1' in reality this is still infinity. A cool way to visualize infinity is to look at fractals and how they keep going to infinity.

This Is The Most amazing and interesting thing to me...
how far do you have to go to reach infinity?(talking about space)
is there infinity? i know you'll never reach an end, but thats what fascinates me about space.
But you must reach an end somewhere. Everything comes to an end right?
And Nothing lasts forever.

One thing that always boggled my mind is that the universe is expanding. Well whats beyond the universe for it to be expanding into?

Infinity is how long this discussion could go on before a definitive conclusion is reached.

infinity exists because the word does.
you don't need to have an idea of content to have a name function as a name.
there are a many ways to get to this, but the one i know off the top of my head is from the meditations on first philosophy: decartes something like i know i am a finite being. finite implies a mode that is it's opposite, so the infinite. so you get to the idea by negation, not because there either is or is not an infinite.

in terms of what it might correspond to, there's an arithmetic type, which refers to the idea that one can never stop counting, that there's always a +1, so it's a way of referring to a very large open ended series.
then there are the other types that folk like to think about, but they're all ways of trying to map onto the world what is implied by the word infinity.
typically it refers to things that are really fucking big.
pascal talks about a second infinity that opens out from things that are really fucking small.

infinity is a fun toy.

I didn't have time to read over this thread- but, according to what you gave as your understandings of the concept, all three are ways of describing the idea through different aspects -a habit in philosophy, and unnecessary I think. Infinity is a way of describing something that is more vast and expansive than one's present knowledge.

I always think of infinity as being bigger than the biggest thing I can imagine, which is a great way to expand consciousness -it's a hippie thing.

Yes

Aristotle writes that if our brain is indivisible, it cannot conceptualize the infinitely divisible except through abstraction. "Infinity" is abstraction. That's why you're having this argument, and that's why it can't lead anywhere.

Sure it exists, but it would take an infinite amount of time to count to it, and infinite amount of space to store it. Do you see the problem yet? It defines itself.

Still don't believe me? Is the universe infinite? Does that mean there are infinite stars/planets? If so, there you have it.

If you answered no, then what happens when you get to the edge? Do you wrap around? Barring cataclysmic events, won't celestial bodies continue to orbit around the universe/galaxy/whatever-their-respective-centers-are indefinitely? Would you call this infinity?

Ultimately, the best proof is the mobius strip, or even simply an ant running on a treadmill. Since it is possible that the ant goes on forever and never reaches a dead end, we have infinity. I don't see how duckznutz can even dispute that.

On this note... It does not work every time; please don't taint the discussion with oversimplifications.

"i don't know" can figure out to "5". Infinity is surely greater than 5, isn't it?

The inevitability of infinity renders being (ie, all that which exists within any context) irrelevant.

I think of infinity as undefinable. To that end, I think of the universe, since it is defined, as definitely not limitless. Space/time is completely limited. Out there past the quasars is a limit. It may be 1 billion billion times further than the quasars we can see, but it's there. Whatever is out there past time and space may be infinite, but that would be beyond any level of comprehension we have, and even mathematics would most likely not help define it. That, to me, would lend credence to it being infinite.

Vigilante: How is the universe defined? How can you show me that it is not limitless? Prove to me that space/time is limited.

How is the universe more defined than running around ball indefinitely, or orbiting indefinitely?

Seems like my examples could clearly be constructed, whereas yours? Tell me exactly how far to go from my house to get to the end of the universe please.

It's pretty universaly accepted that the universe is expanding. Since it is expanding that would lead you to assume that there has to be an edge or end of the universe. What the universe is expanding in to I don't know.

Exactly. It started as nothing and exploded into everything. Gravity weakened, magnetic force remained the same, the laws of thermodynamics as we understand them settled in. Particles settled into Hydrogen atoms and stars were born when the combination of gravity and inward and outward pressure dieselled them into giant nuclear reactors. All other elements aside from helium formed when they exploded.

Everything that we have now has a timeline. Time/space has a timeline. Gravity has a timeline. It is in that timeline that we know that the universe is 14 billion years old. Our entire realm, plane of existence and everything we know has evolved over 14 billion years. That's it. Just 14 billion years. With that known, the universe is very limited. It may be bigger than we can imagine, but it is definitely limited none the less.

Universally accepted doesn't mean it's true. (see: earth is flat)
Fallacy: Appeal to Belief

We are in the realm of hypothesis and conjecture. My point is that you can't just outright prove that it's not infinite, and proving that it's finite does not actually preclude the concept of infinity. It could exist infinitely in time and only be the size of a teacup.

Furthermore, and slightly off topic, if the universe is not infinite, what happens when you reach the end of the universe (see: Douglas Adams, Hitchhiker's Guide to the Galaxy)

Lemme know when you guys get to the end

The only correct person in a discussion like this is the person who believes some variation of "I don't fucking know."

I don't think that's either constructive or in theme with this board. Philosophy means love of learning.

I offered my philosophical perspective. I will readily admit that it is more a statement about rational empiricism than the existence of infinity.

As much as I appreciate the irony, your philosophical perspective doesn't say much and can be viewed as a paradox.

V=HoD. This is the equation that measures the rate at which the universe is expanding. It is a measurable and observable fact. It is not just conjecture. And you could theoretically reach the end of it, it's whats beyond the universe that's the big question.

What is That Which Occurs in the DMV Whenever You are Present?

...

It's a concept. Like zero.

It's there... but it's not.

@rahl: Then wouldn't whatever it is that's beyond it be infinite? But anyway, I think this is really digressing from the point.

Is infinity a number (loosely), a unit, or something else?

I argue that it's a number, that is, it's numeric and requires a unit. In which case it follows that you can have:

• ∞ meters
• ∞ seconds
• ∞ minutes
• ∞ revolutions

If you posit that the universe is limited, and nothing that is measurable can extend past the universe, that means that you cannot have an X that is ∞ meters.

In order to prove that infinity does not exist, you must prove that there cannot be ∞ seconds for something... ie that it can't be the case that the existence of A has a starting point (in time) and no ending point, ever. You must also prove that something cannot revolve, rotate, or otherwise move cyclically for an infinite number of times. (a corrolary of the second point)

I'm tired, so I'm sure there are some categories of measurement that i've left out; feel free to append to this list.

I was referring to post # 72.

Infinity is a useful concept. That is all. It exists at least as much as a leprechaun does in that both are concepts. But this kind of existence isn't interesting since you can't ask whether it infinity exists conceptually without answering your own question.

Any guesses as to whether it actually exists outside the conceptual realm are just guesses. When a person guesses, it is because they don't know. The only certain statement regarding the actual existence of infinity is "I don't know."

And I also might add that mathematical proofs don't necessarily always describe how things occur in reality.

It's almost 3AM, I just got off of work, and I'm pretty tired too.

Right.

• ∞ meters - Impossible, since the physical universe is limited
• ∞ seconds - Impossible, since time has a beginning that we can prove mathematically, and there must have an end, which math seems to uphold as well
• ∞ minutes - See above
• ∞ revolutions - Since time/space is limited, so are the revolutions of any object in our reality.

Basically, in our universe, there is no infinity. I can think of one possible exception, however. This is high speculation on my part.

If:
the universe formed from the big bang
it is expanding
black holes exist
When a black hole dies, it explodes, giving off massive amounts of energy and particles

Then:
it is plausible that eventually the universe will collapse onto itself
if it does, the resulting black hole of everything would continue to exist until all matter was consumed
the resulting explosion would be the big bang of the next universe

And thus the cycle continues. In that, something could be infinite. Not time, not space, not particles, but something.

in principle, the notion of a continually expanding universe is infinite in the same way that the series of numbers is infinite. so for any number n, there is an n + 1.

it is, i suppose, possible that our universe is an aspect of a relative trivial structure within a higher-order system or system of systems. i like to think that we're maybe part of a lima bean or part of a molecule in the upper left corner of a cheap candelabra in some giant mobile home.

personally, like i said i think the infinite is a negative concept, the product of negation, a purely formal construct. what's interesting how more how it's used, so what it comes to mean for communities, how different frameworks impact upon projections as to what's Beyond or Other in this way. it's also interesting to think about why it is that not all symbolic systems include a notion of the infinite. so it's a particularity.

I would like to see the proof that "math" (quoted for ubiquity) has to offer for the universe having an end.

To me it seems that if you consider the universe it could be the geometric equivalent of a ray. A start point, but no end point.

Infinity doesn't always have to be in the extreme sense. Say you have a machine where you press a button and it gives you a random number. Couldn't it give you an infinite sequence?

No offense meant, but go ask Steven Hawking or Google's equivalent. I'm not a mathematician and I don't have time to go find equations or research it. Wikipedia, the free encyclopedia can probably help you in your quest.

Ironically, I just watched a naked science episode while eating lunch, where they discussed the same topic. In the end a supermassive black hole of everything, and possibly the death of the universe and the beginning of a new one when it popped. Cool.

A start point of a ray implies an end, even if one end. Even in concept, not infinity. There can be no end, in either direction. By that, forwards or backwards in time, or on a linear scale of any other measure.

No the machine couldn't. The machine is limited by it's physical components, and pulling the plug. If that's not enough, the machine must last forever and spit numbers forever and this realm, this universe, will not last forever. Even if the machine could overcome all obstacles of this universe, the laws that govern the universe itself would destroy it.

So could it simply spit out "∞"? Sure. But that is not a number sequence. Also, the number sequence has a beginning. Say it began with 3. It couldn't be infinite, because it has a beginning in time and concept. In the end, it is still constrained by the universe around it.

I assume we are talking about reality here. If not, one could devise infinity in any number of ways. We could be a simple observer, floating outside of space/time with an infinity-spitting machine, tossing numbers outside of time in a circular existence as the universe expanded and collapsed for all of your existence. But then another question comes up. How long did you exist?

Heh.

manwithaplan: were you talking about my post or something else?

i'm confused.

No roach, I was referring to Vigilante's.

Vigilante. No offense taken, but if you bring something up here you should make more of an effort to defend it than saying "google it". I mean, I could just say google this whole discussion and end this thread.

I disagree with your definition of infinity. You're trying to disprove the notion based on what I consider a non-standard definition of the subject matter. Who said infinity has to go on in both directions?

Also, formally, my infinite sequence machine example is such:
If infinity exists
There can exist such a mechanical device that will produce an infinite number sequence
over an infinite amount of time.

It doesn't have to be electronic. That's not fundamentally part of it. You can't say it will fail because there won't be enough time, because the statement operates under the assumption that there is infinite time.

The task is to prove the opposite to form a biconditional. I feel like it's a biconditional by definition, because an infinite number sequence would take infinite amount of time. So if one exists, there must be infinity.

This statement by be cyclically redundant and therefore invalid though, but I challenge somebody to formalize the opposite viewpoint.

To me the statement you made on the machine, and thereby implying infinite time, is like trying to make the sky green because you want it to be so.

If you want to make your own reality, the conversation quickly loses interest (for me). I'm trying to go by what documentaries and such have discussed, not choose-your-own-adventure. That's just my take on the topic. If you want to go random on me, that's fine. I just lose interest :)

The symbol for infinity has no beginning and no end.
∞
That is the definition of infinity I am talking about. Not a line with a starting point. "∞" has no starting point. If you start somewhere, anywhere, you have lost infinity.

To me, the only thing that might have an infinite definition in this universe is gravity and other universal/molecular forces. Gravity brings about the crushing of the universe. Presumably, it is back when the big bang happens again. It can't be tested or proven, but logic dictates that it remains. Otherwise how could the big bang have occurred?

Not to nag, but I have 3 hours of free time a day, and 4 if I lose sleep. I don't want to spend it researching a given topic when I could be looking at porn or something.

Sorry if someone mentioned this already but there are min maxes to energy (and therefore matter and all that exists). Plank's constant to speed of light. In other words, your example is flawed. There is a minimum distance one can travel. So it would not take infinity to get there.

I think infinity as a theory/practical math application exists of course. But no, to us infinity does not really exist. Everything, everywhere dies.

11 dimensional terms? If you're referring to string theory, that's not widely accepted. In fact, it's mostly believed to be false. It would not be fair to use that in this discussion because it does not fall into the set of common terms and beliefs that we all share.

Zeraph - Your approach is umm... I can't think of a better word than egotistic. I don't mean it in a negative way... just that it pertains to the ego of living things.

The world was around before you were born, and will probably be around after you die my friend. So just because you're not infinite in longevity does not mean that something else cannot be.

Yes, if you completely ignore the way the universe is behaving. Well duh, of course we die. The universe will too, it's just not there yet. Are you completely ignoring the observations every physicist/cosmologist/astrophysicist/etc in this field of study has made and generally agrees upon?

No. But it seems I shouldn't expect you to actually read what I'm saying once you've made your mind up on what you think I mean.

My last post never made a claim that the universe is infinite. I'm simply disputing the reasoning that because people die, nothing is infinite. However, I should caution you again against the arrogance of simply believing whatever it is "every physicist/cosmologist/astrophysicist/etc" believes (and I doubt very much that every man more learned in the field than you or I believe this). After all, was it not Galileo who was punished for declaiming the flat earth theory? We never know, and as far as I'm concerned this theorizing is inconclusive, and more importantly IMPERTINENT to this discussion. So kindly, please drop it.

One of us is misunderstanding this discussion. I see this as a hypothetical question of concept and potential. Your argument, as I see it, is that because the universe will end (according to popular opinion), nothing can be infinite.

To this, I say, what if you have a yard stick and you cut half of it off. Is it still a yard stick?

Better example: If a bullet is flying and you lift up a piece of metal and block it half way before it reaches its target. Can you not make a projection of where it would go?

So even if the universe ends, precluding an infinite process, motion, etc, is it wrong to call it infinite?


----

also, @zeraph and @meri

I don't think meri was being literal. It's a hypothetical principle used to outline certain flaws in logic. It was first introduced to me in calculus class when studying integration and derivation, because those deal with infinitely halving things.

Yeah I jumped the gun a little. My bad.

I know every person in the field does not believe the same thing. Even as I typed "every", I was thinking of a documentary involving the constant C changing over the course of the expansion of the universe.

In some way perhaps the universe is infinite. If it recycles, then the forces involved would most likely remain familiar. Gravity, electromagnetism, various molecular forces, etc. have no reason to deviate, especially if when a black hole spews matter at it's collapse, the resulting energy and mass behave as everything else. Some things could deviate though, in some minor way with profound results.

I don't know. The more I think about it, the more I argue with myself. Arguing with yourself can get boring real fast.

The speed of light is also different through different substances. Seeing as how we know very little about what is at the 'edges' / far reaches of the universe, we can't tell for sure what the speed of light there is, or what material alters it. Black holes are also fabled to be able to bend the path of photons, which seems to me like it would modify their speed (not just velocity vector).

I don't think it's necessary to consider the universe when considering infinity. Instead of taking the object of question and casting it in the light of things we know, what we, in this thread, are doing is casting it in the light of things we actually know very little about.

The concept of infinity is older than our knowledge of the universe, so surely we don't absolutely need modern science to answer the question, do we?

Before modern science there was religion, and not much else. I don't know the history of infinity and I'm not looking it up (I leave for work in 45 mins and I'm not spending it at this desk). It's not much different now, but we can apply new rules to it. Sure we can apply God to this concept and say God is infinite in all ways, but that brings us no closer to realizing the concept.

Unless you had something else in mind. If so, do tell :)

Also, the speed of light is different through substances because of molecular interference. C defines light as light in a vacuum. Playing bumper cars does not change the speed of light.

First, I did mention the practical math applications that it does exist in. Second it is only living things that experience, so what does infinity matter to a living thing then since it is something that it cannot experience? Yeah, the universe was around before living things, but what does it matter if there is nothing alive to perceive it?

If a tree falls in the woods when no one is there to hear it, does it make a sound?

Somehow I knew you were going to end on the tree-falling allegory. You're talking about a different question: "Can we experience infinity?" The clear answer to that is No, and it does not even need a discussion. Once again, I interpret the question differently. If we're to discuss this perhaps we need to start by making a more specific question that we can all agree on.

Not in this realm. Not trying to bring personal spirituality into this. Just saying.

Well, here's a fun question for you:

Is an infinite process infinite only when its duration reaches infinity, or is it infinite from the start provided it will reach infinity?

so let's assume that there is something more to this notion of the infinite than an empty space hollowed out by the word "infinite"...

why would something infinite be singular?

same kind of question: what lets us assume that there is *a* universe? why aren't there any number of them?
the explanation's not in the universe, but in the word "universe" yes?

I'm afraid I don't really follow your question. Nothing we have said rests on their being a single universe. There could be several infinite ones separated by dimensions, or otherwise. if they were juxtaposed in 3-space, then they could not be infinite but would not be separate universes but part of the same universe.

the universe was an example.
the point concerned the notion of infinite-ness and what relation it could possibly have to a singular process.
i know the answer, really: the idea of an infinite process is a transposing of that of the number series in general, so another version of for any number n there is always n+1

i just thought it curious that we talk about "an" infinite anything.

the main point is i see little in this beyond playing about with the hole created by the word infinity, which requires no referent and no knowledge of a referent, a hole generated through relatively simple acts of semantic inversion or negation.

but still, how exactly does a single infinite process make sense?
if the process is itself singular, it can't be infinite---it can be endless. but endless and infinite aren't the same are they?
except if you adopt the position that the number series is a model for the infinite.
but that seems kinda trivial, in my humble opinion.

just poking around.