i absolutely hate this thread. and the sad thing is, i started the first one :(
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i absolutely hate this thread. and the sad thing is, i started the first one :(
Indeed!Quote:
Originally Posted by lefteyewilly
And so far i have only seen proof that three thirds of one equals one.
And that our math system cant properly work with a number that has an infinite number of digits after the decimal.
random25: I agree that maths might not be perfect but let's not go on and blame it again and again from time to time. Rather looking at the downside of it, I rather look at what remarkable and astounding position maths has got us in the current world. I know I sound geeky/angry/lecturer type, but hey, maths is one of the reason why we are posting on this 'forum'.
i have to jump in and give my opinion about this subject since i am a math nerd. like a few of you here, haha.
to me 0.999...!=1
it comes down to basic calculus and limits. the limit of 1/x where x>0 gets infinitely smaller and closer to 0 BUT NEVER reaches 0. so i am thinking that somehow 0.999...+p=1, p=lm 1/x?
would i be wrong in saying that? since 0.000...1 does not exist, and 0.999... does not equal 1, so there must be a describable gap between 0.999... and 1. the gap is an infinitely small number, hence the limit of 1/x.
now i know that i havent had calculus in a few years, so my exact explanation of the limit of 1/x is probably wrong, but you get the point. that gap is an infinitely small number.
just my 2 cents :)
I do enjoy such in depth debates on such theoretical problems like this.
I will never believe that 0.999... = 1,
because i know that we are all way to primitive to truly grasp what these numbers actually represent.
Any one that says that they do completely understand what these numbers actually represent, and imply that they can do math with them is wrong, and too primitive to understand that they are too primitive to truly grasp what these numbers actually represent.
And that is my 0.999... cents.
I find that kind of funny because that talks about gps and goes on to explain about how there are 4 problems with using special relativity or general relativity. Lorentz is the theory that I forgot about and is the one that works with the GPS.Quote:
Originally Posted by ihoss.com
There is nothing in between 1 and 0.999... If you can say that then you are thinking in terms of time. It's like saying that there's an integer between 1 and 0. I think that until we die (unless you are an atheist or have a religion the goes against this or we get a better math system) and know most if not all the secrets of the universe then this will always be argued. By our math system which is an abstract idea not a tangible object you can deduce that 0.999... = 1 or you can argue that it does not. This is an abstract idea. You can never be sure that an abstract idea is a 100% correct. Even for the laws of gravity. We know that there is gravity and we know how to project it good enough but it's still a thought. Until we can attach to each theory or idea that it's the absolute truth, we can't state it as a fact. This is not one of the ages past where you would take any common knowledge at face value. It's too comfortable to do that. Take nothing for granted.
Hello! I already declared Yasunobu the winner of this. :D
Do we need to make two versions of math to make everyone feel good the same way schools sometimes play with grading systems to avoid giving Fs? Ok. We'll have the one version that all serious scholars of math subscribe to and then the friendly, gentle one where 1 only equals 1 because 0.999... looks different and that is just way too confusing!
Do some research. You can disagree and even find an occasional nut in a forum that will agree. But, virtually every person qualified to confirm this point agrees that 1 = 0.999...
Look here:
http://en.wikipedia.org/wiki/0.999...
http://www.relativesanity.com/archive/192
http://www.purplemath.com/modules/howcan1.htm
and my favorite, a lesson for little kids:
http://www.mathsisfun.com/9recurring.html
Perhaps the more interesting part of this debate, why people have such a hard time accepting this fact, is touched on in the purplemath link (just before proving the fact from several perspectives):
Had to add this part as well in response to this "leapfrog" theory of a number "getting closer". Numbers don't move.Quote:
There are many different proofs of the fact that 0.9999... does indeed equal 1. So why does this question keep coming up?
Students don't generally argue with 0.3333... being equal to 1/3, but then, one-third is a fraction. Maybe it's just that it "feels" "wrong" that something as nice and neat and well-behaved as the number "1" could also be written in such a messy form as "0.9999..." Whatever the reason, many students (me included) have, at one time or another, felt uncomfortable with this equality.
One of the major sticking points seems to be notational, so let me get that out of the way first: When I say "0.9999...", I don't mean "0.9" or "0.99" or "0.9999" or "0.999 followed by some large but finite (limited) number of 9's". The ellipsis (the "dot, dot, dot" after the last 9) means "goes on forever in like manner". In other words, "0.9999..." never ends. There will always be another "9" to tack onto the end of 0.9999.... So don't object to 0.9999... = 1 on the basis of "however far you go out, you still won't be equal to 1", because there is no "however far" to "go out" to; you can always go further.
"But", some say, "there will always be a difference between 0.9999... and 1." Well, sort of. Yes, at any given stop, at any given stage of the expansion, for any given finite number of 9s, there will be a difference between 0.999...9 and 1. That is, if you do the subtraction, 1 – 0.999...9 will not equal zero. But the point of the "dot, dot, dot" is that there is no end; 0.9999... is inifinte. There is no "last" digit. So the "there's always a difference" argument betrays a lack of understanding of the infinite. (That's not a "criticism", per se; infinity is a messy topic.)
Quote:
This "getting arbitrarily close" process refers to something called "limits". You'll learn about limits later, probably in calculus. And, according to limit theory, "getting arbitrarily close" means that they're equal: 0.999... does indeed equal 1.
As I was saying earlier, this has already been debated and decided. The decision was 0.9999.... == 1 returns true. FlashLacky basically stated a lot of what I was trying to explain.
Maybe it's best put like this:
1.000... - 0.999... = 0.000...
1.000... - 0.999... = an infinitely small number. If it best suits your purposes to pretend that an infinitely small number is equivelant to 0, go ahead. But by defenition of inifinity itself, an infinitely small number, while however mathematically intangible, will always remain SOMETHING above 0.
1.000... - 0.999... != 0.000... / 0.333... != 1/3 / 0.999... != 1
:D
The tribe has spoken. Go back to your business.
Seriously though, this could be disputed forever, due to varying opinions and theories about the mechanics of inifity. Where you see 0.999... expanding infinitely into a whole number, I see an infinitely expanding difference. That difference isn't just made irrelevent because we can't process something without an end.
It doesn't matter that experts agree one way or another. It's unprovable.
I think the problem is that infinity really does'nt exist in the real world, it's just a human made construct, an idea, a philosophical theorem. Because of that, if you start depending on it in your math, you can only fail.Quote:
Originally Posted by plang
Fredi
It does exist in the real world. It just doesn't exist in the world that we can mentally encapsulate.
Fine, tell me what the edge of outer space looks like when you get there. :)Quote:
Originally Posted by Fredi
Black, no light, no radiation, nothing. But you never get there, it's impossible. Only light from the big bang can reach the edge (or be the edge).
@plang: where?
Fredi
You're talking as if going the speed of light is imposable. Tell me what experiment shows this.
If you have mass, reaching the speed of light is impossible by definition. Just ask the CERN.
Fredi
It exists in lots of ways. Take a look around the room you're in. There's an infinite number of points in space right in front you.
It just falls appart when we apply mathematics to it because equations need finite numbers for our heads not to hurt. When you use infinity in Maths...well, like you said; it doesn't really fit properly. It's so abstract that it becomes open to interpretation and cannot be proven either way. It falls to personal belief and perception.
A point in space is just geometry, it's not something that actually exist, it's just a construct to apply our formulas.Quote:
Originally Posted by plang
Geometry, math != reality
Fredi
Yes. We could debate subjective concepts of infinite all day. The real questions to ask are what definition of infinite is most useful to us and which is the most well founded? That definition has, in fact, been worked out at least to the point where the vast majority of people who must deal with the concept on a serious level agree on ONE well thought out interperetation. See Axiom of Choice.Quote:
Originally Posted by plang
So, you can choose to see infinite differently than everyone else, including all of the people whose ideas mathematics and most sciences are based around. Certainly, that is your perogative. Has this tribe yet mastered fire?
Anyway, there is no such thing as "infinitely small". "Small" is a relative term. What do you mean by small? Small to me might mean the size of a pin-head. But, to an ant, a pin-head might mean medium. 1-.2345 results in a value that is no more deserving of the word "small" than it is "medium", "large", "purple" or "blue".
Again, I think the best way to demonstrate that 0.999...= 1 is to simply sit down and start doing the math on:
1.000... - 0.999...
Try it out! Keep carrying over that one about thirty times. Pretty soon you will realize that '...' means the one never happens. There is no limit exception for infinite. Infinite zeros means all zeros. No eventual 1.
Yes, when you look at it -- i.e. when the observation has taken place. But it's thesame quantum mechanics that say that when an energetic particle isn't observed, or rather, when the place is unknown, it exists at an infinite amount of coördinates in space, only to "choose" a coördinate when observed. That's superposition for you.Quote:
Originally Posted by Subway
Why infinite? It only exists at the coordinates that it can possible choose, not an infinite amount of coordinates. Where did you get the idea that it can choose an infinite amount of places?Quote:
Originally Posted by wouter999
The (imaginary) cat isn't dead, alive and everything inbetween either, it's dead and not dead at the same time or if observed, one of the two options. Same for the spin of a particle. Two options. Same for the position of an electron circling around an atomic core, it can only take one of the (relatively limted) possible positions.
Fredi
How can an electron spinning around a core have a limited amount of possible locations? As far as I know, a circle trajectory has an infinite number of possible points, it's the fundamental basics of a circle.
Yes, Schrödinger's cat is both dead and alive, and a particle is in both up and down states, but those are superpositional sets of a value 2. However there are many superpositional sets where the amount of states superimposed on eachother is infinite. Think of the double slit experiment, where one electron is shot through two slits: how can it interfere with itself if it is not in every possible location? And there are an infinite possible locations, that's a rule of any spatial body.
no one knows the size of space, so how can coordinates be finite. Sure an electron hovers around its atom because its bound by a force of some kind, but say that force is removed, it can go anywhere, be anywhere. Someone said it before, nothing is proven so we should assume infinite possibilities. And your forgetting the possibility of parallel universe's, so something is not bound by x,y,z but another value. Maybe its u value. And this value could be anything.Quote:
Originally Posted by Subway
i'm currently
x:10923084092384023844023984023480, y:123270137812039812731023981290138091283021983, z:9923878937192873987291378912873917,
u:1
But i'm also at
x:10923084092384023844023984023480, y:123270137812039812731023981290138091283021983, z:9923878937192873987291378912873917,
u:2
You can add as many dimensions as you want, as long as you don't add an infinite amount of them, anything will still be finite.
"Every possible position" is only infinite if you apply geometry (math) to it. In reality, the amount of positions is always finite, defined by the exact properties of the electron(s)/proton(s)/or whatever else you use for your experiment. Now of course you don't know the exact properties of each element, but that does'nt meen those don't exist.
If you take out (of reality) one single electron and remove any forces to it than well, it's just like math and geometry, it's imaginary, not anymore bound to reality. In reality nothing is isolated from the rest, we live in a holistic universe after all (again, quantum mechanics).
Fredi
Wow. 4 pages since yesterday evening...
This has far departed from it's original purpose. :(
exactly, so anyone saying 0.999... is absolutely equal to 1, is just as wrong as anyone saying 0.999... is absolutely Not equal to 1.Quote:
Originally Posted by swak
We are all to primitive to really know the truth.
To some it looks like 0.999...=1, to some it looks like math is flawed.
Trying to prove that math is not flawed by using more math that maybe flawed will not ever work.
No one can ever win this argument in the same way no one can prove that i exist.
I'm sorry, but those infinite zeros are fooling you. Think about the 9s. It's easier. Carry those 9s thirty times and tell me at which point you get a freakishly big nine that brings about your whole number.Quote:
Originally Posted by FlashLackey
The 9s go forever, infinitely falling short of 1. You can't subtract 0.999... from 1 and expect a reasonable answer that makes sense. It's just (in my opinion) and incorrect argument.
Infinity is abstract, while 1 is not. 0.999...is an interpretable idea - a philosophical construct even, and by its own bizarre nature, is clearly not the same thing as 1.
In your applied maths it might "more or less" equate to 1, for the purposes of ignoring a difference that has no practical effect, but the statement 1==0.999... is simply not the absolute truth.
Just stumbled over this at /. ... too funny:
Q: Do you consider photons particles or waves?
A: Yes.
:p
Another one:
:pQuote:
Most quantum computers have to be isolated from the outside world (look at them and they stop working)
So... in what fundamental way is this different from running Windows?
All taken from this quantum computer post: http://science.slashdot.org/science/.../1355255.shtml
Fredi
This is sadly where it falls to semantics. You can't tell me I'm wrong, because you can't prove it. You can only cite maths that relies on the same belief it tries to prove. It's circular and meaningless.
Random has it nailed in this regard.
Oh wait, that quantum joke works perfectly for this thread:
Q: Is 0.999... less or equal than one?
A: Yes
:p
Fredi
Quote:
Originally Posted by plang
I don't get how you can keep saying that when the number 1 is non-existent. No matter what you're not going to be walking along one day and say "hey look, it's number one!" and be referring to something other than a symbol. 1 is just as abstract as infinity but infinity is just too much for us to grasp because everything we can see or feel is finite. Even outer space can only be finitely. The best way I can imagination space is as an ever expanding object.Quote:
Originally Posted by http://www.google.com/search?q=define%3A+abstract&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a
Going by math, calculating 1=0.999... is just as abstract as stating that 1=0.999... I think that the argument can either be determined by saying: "Look 1 does not equal 0.999... they are two completely different numbers separated by a minuscule difference." or "1=0.999... is a fact because by the same math that we use to calculate gravity and some other physics we can determine that they do equal each other. 1/3 * 3 or 3/3 = 1 and 1/3=0.333...*3=1 or 0.999.... Pretty much the only way you can say that 1!=0.999... is by disregarding our most fundamental math system which in turn forces us to disregard anything that results from it such as calculating gravity or calculating the proportions of a building. I think that there is really no real way to resolve this because we are dealing with the abstract and no experiment will determine one way or another. I also think that this will be debated till the end of time with each new generation until it becomes widely known and agreed upon and accepted. This has already been debated before and yet, here we are debating it some more.
This is interesting though, it's a good debate. Debating is interesting and this is a great debatable subject to engage in. I wish that I had more debates like this in school but I don't think that I'd do as good unless I know what I'm debating about pretty well.
By the way..."Infinitely small" was relative to the number 1. A 'number' greater than 1, but by an infinitely small margin. If you don't believe in this number, then you should also not believe in the existence of 0.999... Because the sum of the two equals 1.
Try to think about it in terms of a jigsaw puzzle. 0.999... has a very tiny piece missing - infinitely tiny infact (wow!). It needs that infinitely tiny piece to become whole again.
Makes my head spin, but I can see it.
Btw, just noticed your postcount. Is it 0 or the difference between 0.999... and 1, I can't tell. :pQuote:
Originally Posted by plang
Oh and a new one for the next six pages of circling discussions:
1 == 0.999...1
Fredi
Yes, saying that 1 is not abstract was a poor choice of words, you're right. What I meant was that 1 is something that has real, clear ties to the very fabric of how we count, calculate, etc...Infinity on the other hand is just something else.Quote:
Originally Posted by swak
And re:debating. I'm not here to try and change the world. I'm just here, in this debate, to challenge my own mind, and to have something to think about, and so on. I accept that I could be wrong, but while I believe that I;m not I'll argue my point with conviction, as long as I have something to say :).
It doesn't really interest me that the debate has been done before. I've never discussed it before, hence it's interesting to me.
Even one of those links that some one posted as a supporting article for 0.999...==1 stated in its first paragraph that the following rationalizations required certain things to be taken on faith.
I don't know about anyone else, but I think FlashLackey and I agreeing on anything is harder to believe than 1 = 0.999...
Heh :). Hey, I forgot my old Flashkit login. Sue me.Quote:
Originally Posted by Subway
Have a look for my infinitely small post though. It's profound.
I was just joking, just to make that clear. Btw, most of my posts are made-up. There was a recount where all CL posts were removed from anyones postcount and the mods got the chance to get those removed ones back. As I did'nt know exactly how many I had, I just guessed a number, so my postcount is at least as imaginary as infinity outside of math. :D
Fredi
I don't think I had many posts on my old account anyway, to be fair :)... When I started learning Flash a couple years ago, I had a brief period of self learning before being thrown in the deep end at a web company. After that I stopped going to forums much because I had all the help and discussion I could handle at work.
Might have to make regular visits to the lounge though if interesting stuff like this comes up. I'll see how long I can keep my post count 0. Simple things amuse me :)