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.