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.