Infinity
Poll
 | 5 votes (23.8%) | ||
| | 8 votes (38.09%) | ||
| | 8 votes (38.09%) |
21 members have voted
if you are talking about math then sure it does.
if you are talking about physical quantities, then its another story.
In reality. Some people think the math is reality right, but it's just a tool to understand reality. I know I've been through this discussion before in my life, but I've forgotten. If infinity did exist in reality, how would reality change? The first ball I bounced as a kid would still be bouncing forever after i died. Mind blowing I think.Quote: andysifwhat exactly are you talking about?
if you are talking about math then sure it does.
if you are talking about physical quantities, then its another story.
Edit to add:
I've probably over forumed myself lately to infinity winding up thinking about this.
Quote: onenickelmiracleDo you believe infinity exists?
No.
Infinity can only exist if there is no limit to quantity, space or time.
Infinity can not exist because unlimited quantity, space or time can not exist.
That reminds me, I'll need to pick up a case of Doritos.
Colorado rocky mountain high?Quote: Sabretom2I'm on my way to Colorado, gimme a day or two and I'll have the answer.
That reminds me, I'll need to pick up a case of Doritos.
Quote: IbeatyouracesSomething about 3.14.......... you get my drift.
Pi is a ratio that goes to an endless number of digits.
There is a difference between 'endless' and 'infinite'
Unlike infinity, Pi is subject to mathematical laws.
What is infinity squared? What is half of infinity? What is infinity divided by infinity?
The square root of Pi is 1.77245 to an endless number of digits.
You can apply mathematical laws to Pi at any point in the ratio.
This is impossible with infinity which has no measurable quantity at any given point.
Quote: TankoPi is a ratio that goes to an endless number of digits.
There is a difference between 'endless' and 'infinite'
Unlike infinity, Pi is subject to mathematical laws.
What is infinity squared? What is half of infinity? What is infinity divided by infinity?
The square root of Pi is 1.77245 to an endless number of digits.
You can apply mathematical laws to Pi at any point in the ratio.
This is impossible with infinity which has no measurable quantity at any given point.
http://en.wikipedia.org/wiki/Transfinite_arithmetic
Quote: onenickelmiracleThe first ball I bounced as a kid would still be bouncing forever after i died. Mind blowing I think.
Arguments will be made that friction and gravity kills the inertia needed to keep it bouncing.
But, assuming the ball hasn't been melted and recycled, as it sits somewhere, the orbits of the electrons in its atoms are still affected by those bounces. And that would be permanently / infinitely. Any additional bounces further change the orbits, but in a combined / compounded way.
Very interesting point. Many on this board say that the only reality is energy-matter which is your basic naturalism, but that doesn't account for math, mental concepts, intention and consciousness in general which isn't material at all.Quote: BleedingChipsSlowlyWhat would be the basis the discussion of this thread if infinity didn't exist? Do ideas and concepts not exist simply because they lack physical form? If so, I've got a ship load of math to forget about.
At one point Ivanova mentions they're running out of time. Zathras, the enigmatic alien who seems to understand what's going on, says "You can't run out of time. Time is infinite. You are finite. Zathras is finite. This," picks up a wrench, "is wrong tool."
Humm...Quote: BleedingChipsSlowlyWhat would be the basis the discussion of this thread if infinity didn't exist? Do ideas and concepts not exist simply because they lack physical form? If so, I've got a ship load of math to forget about.
Following your argument, unicorns exist.
The human mind can make up things that do not exist in the physical world. Saying they "exist" is changing the meaning of the word "exist". The etymology of "exist" is clearly "ex" (outside us) "sistere" (stand).
Saying infinity "exists" in math is akin to saying square root of 2 exists, cosinus exists, i exists, ∫(x) exists, π exists.
π is a theoretical limit of a ratio that is rational in the real world, because of the lower bound imposed by Planck's elementary quantum of space or matter.
Not !Quote: IbeatyouracesThey're the same.Quote: Tanko
There is a difference between 'endless' and 'infinite'.
A Möbius band is endless but not infinite.
Quote: kubikulannHumm...
Following your argument, unicorns exist.
The human mind can make up things that do not exist in the physical world. Saying they "exist" is changing the meaning of the word "exist". The etymology of "exist" is clearly "ex" (outside us) "stare" (stand).
The hippocampus in London taxi cab drivers was shown to be larger (than average) and grew even more with longer time on the job. Now if they had to absorb the info and travel of several mythical worlds, such as driving in a simulated world in game play perhaps their heads would grow to giant tumor size if you surgically removed the skull to let the brain expand..
I'm not sure that that implicates a direct correlation to existence.
(Or maybe I'm kidding.)
Quote: kubikulannHumm...
Following your argument, unicorns exist.
The human mind can make up things that do not exist in the physical world. Saying they "exist" is changing the meaning of the word "exist". The etymology of "exist" is clearly "ex" (outside us) "stare" (stand).
Saying infinity "exists" in math is akin to saying square root of 2 exists, cosinus exists, i exists, ∫(x) exists, π exists.
π is a theoretical limit of a ratio that is rational in the real world, because of the lower bound imposed by Planck's elementary quantum of space or matter.
The concept of a unicorn clearly exists. You and I both know what we mean when we say "unicorn," and it probably means this:
That is an image of a unicorn. I can point at that image and say "it exists."
That said, no unicorn is ever known to have existed in real life, only in facsimile. Animation, creative photography, etc.
Unlike "a unicorn," which is a noun, "infinity" is a secondary noun formation of the adjective "infinite," with the definition of "not finite." Finite is well-defined, and as a result so is "infinite."
There is no such thing as "an infinity" or "the infinity" in the same way there is such a thing as "a unicorn". You can draw a picture of a unicorn and say "there is a unicorn". You cannot draw a picture of "an infinity" and say "there is an infinity." However, the concept or idea represented by "infinity" very definitely exists, in the same way as the concept or idea represented by "five" (or "5") exists.
Quote: onenickelmiracleDo you believe infinity exists?
Do you believe that four exists?
The image exists. Not the unicorn it represents. If it is the image of some wood or plastic simile, that doll exists, but not what is commonly defined as a unicorn.Quote: MathExtremistThat is an image of a unicorn. I can point at that image and say "it exists."
I am precisely saying that being well-defined is not a sufficient (or necessary) condition for existence. "Unicorn" is well-defined. "A red square cucumber" also.Quote: MathExtremistUnlike "a unicorn," which is a noun, "infinity" is a secondary noun formation of the adjective "infinite," with the definition of "not finite." Finite is well-defined, and as a result so is "infinite."
Drawing a picture has nothing to do with existence. Either way. The picture exists. Not necessarily the thing it represents.Quote: MathExtremistThere is no such thing as "an infinity" or "the infinity" in the same way there is such a thing as "a unicorn". You can draw a picture of a unicorn and say "there is a unicorn". You cannot draw a picture of "an infinity" and say "there is an infinity."
What I'm thinking is that saying that "a concept exists" or "an idea exists" is an abuse of the term "exist". Using it in this way can lead to self-reference paradoxes. Along Tarski'a approach, you should define language levels, and specify at which level you define "exist". Clearly saying "the unicorn exists" or "the concept of a unicorn exists " are two very distinct uses of the word "exist", aren't they?Quote: MathExtremistHowever, the concept or idea represented by "infinity" very definitely exists, in the same way as the concept or idea represented by "five" (or "5") exists.
But this conversation is simply a rehash of the (in)famous ontological "proof" of the existence of God. "Because it is conceivable, then it exists." Tautology.
Quote: kubikulannWhat I'm thinking is that saying that "a concept exists" or "an idea exists" is an abuse of the term "exist".
But this is precisely how the term "exists" is used in mathematics. It wouldn't make sense to use it any other way, because mathematics is nothing more than theoretical concepts.
I think that it's generally ok if the meaning of technical terms diverge a bit from their common-english meanings. The problem comes when people conflate the two meanings, which is exactly what the OP is doing.
Yes, I can agree with this. Note it is similar to what I say about "levels of language".Quote: AxiomOfChoiceBut this is precisely how the term "exists" is used in mathematics. It wouldn't make sense to use it any other way, because mathematics is nothing more than theoretical concepts.
I think that it's generally ok if the meaning of technical terms diverge a bit from their common-english meanings. The problem comes when people conflate the two meanings, which is exactly what the OP is doing.
Typically, when in a theorem we use the phrase "there exists an epsilon such that etc.", we are not referring to the real world but the special world of theoretical concepts. In that context, we may write "there exists an infinity of prime numbers".
( But even then, are we not stating the existence of the prime numbers, not the "existence" of infinity itself? )
I would characterize it as an abuse of language. Mathematicians would be well-advised to say "there are an infinity etc." instead of "there exists". But mathematics uses many such everyday words in a totally different meaning. "Group", "building", "root"...
So you either have infinity existing or you have existence, but you can't have both at the same time. Maybe if two infinite forces cancel each other out maybe, but it seems the same as not existing.
Quote: onenickelmiracleFour can't exist independently. If infinity could actually exist in reality, the universe would still be banging, never stop, and nothing would exist if the original sequence never stopped. With infinity being real, nothing can eventually happen.
So you either have infinity existing or you have existence, but you can't have both at the same time. Maybe if two infinite forces cancel each other out maybe, but it seems the same as not existing.
Please define "infinity" and "exist". You are not making any sense.
"Infinity" is a theoretical mathematical concept.
You have said that you want to use "exist" in the physical sense.
So, no, a theoretical mathematical concept does not exist in the physical sense. "Infinity" does not "exist", and neither does "four"
Quote: kubikulannI would characterize it as an abuse of language. Mathematicians would be well-advised to say "there are an infinity etc." instead of "there exists". But mathematics uses many such everyday words in a totally different meaning. "Group", "building", "root"...
I think the issue here is that non-mathematical language has, in some instances, co-opted words with purely mathematical origin and attempted to give them everyday meanings. "Infinity" does not have an independent, everyday meaning the way "group" or "root" do. The only proper meaning of "infinity" is a mathematical one.
1Quote: TankoWhat is infinity divided by infinity?
Case closed. Infinity exists in large numbers ;)
Quote: NareedIsn't there a car called "Infinity?"
Nope. That's Infiniti.
I don't think your inference that a concept implies physical existence can be drawn from my statement, but I get yourQuote: kubikulannHumm...Quote: BleedingChipsSlowlyWhat would be the basis the discussion of this thread if infinity didn't exist? Do ideas and concepts not exist simply because they lack physical form?
Following your argument, unicorns exist.
point. Sometimes that is exactly what is intended. Let's do mix string theory and dark energy/mater into the thread!
I have just placed two equal-length straws on a table such that their barrels form a right angle and one tip of each is touching the other. Now then, following your line of reasoning I am having a hard time describing the distance between the two other tips. If, in fact, that distance exists at all.Quote: kubikulannSaying infinity "exists" in math is akin to saying square root of 2 exists.
I'm not sure but think it would be undefined since it could be 1 or infinity.Quote: BleedingChipsSlowly1
I seem to recall substituting 1 for infinity divided by infinity as being allowed for some limits work. It's been a few years. I also recall a number being divided by infinity as being considered "virtually" zero for the calculus.Quote: onenickelmiracleI'm not sure but think it would be undefined since it could be 1 or infinity.
It's been ages I can't be sure of much.Quote: BleedingChipsSlowlyI seem to recall substituting 1 for infinity divided by infinity as being allowed for some limits work. It's been a few years. I also recall a number being divided by infinity as being considered "virtually" zero for the calculus.
Are you addressing me? My statement was about n/x = 0 for x-> infinity. You might want to rethink your statement.Quote: MangoJ(2x) / x = 1 for x -> infinity ? You should rethinkn your statement.
Quote: BleedingChipsSlowlyI seem to recall substituting 1 for infinity divided by infinity.
Yes, this was adressed to your statement above. It doesn't even work for anything.
Quote: BleedingChipsSlowlyAre you addressing me? My statement was about n/x = 0 for x-> infinity. You might want to rethink your statement.
You wrote:
Quote:I seem to recall substituting 1 for infinity divided by infinity as being allowed for some limits work.
which makes no sense.
Sometimes the limit of f/g is 1 as both functions go to infinity. Sometimes not, as Mango gave an example of.
Quote: MangoJ(2x) / x = 1 for x -> infinity ? You should rethinkn your statement.
The question was x/x for x -> infinity, not 2x/x.
(2x)/x = 2 for x -> infinity.
If I pour a bottle of water into a bucket, and I were able to capture an image every time a bit of water moves, even a single molecule, then I would have an infinite amount of images.
If I were to plot every number between 1 and 2 on a number line, I would have an infinite amount of points plotted. There are infinitely many numbers between 1 and 2.
plus one day !Quote: NareedHow about Eternity?
What you describe, what mathematicians describe since the time of the Greeks, is the ideal form of a square triangle. They define a purely theoretical equality between the two straws, a purely theoretical right angle and a purely theoretical irrational quantity.Quote: BleedingChipsSlowlyI have just placed two equal-length straws on a table such that their barrels form a right angle and one tip of each is touching the other. Now then, following your line of reasoning I am having a hard time describing the distance between the two other tips. If, in fact, that distance exists at all.
Before your eyes, you have two straws that are not physically equal in length, not at a purely exact right angle. And the physical distance between the tips (whatever that means: how do you measure the exact place of the tip?) is forcefuly a rational number in terms of quanta.
