The Truth
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 damienthebloody
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it's similar, but there is an important, subtle difference that i'm currently too tired to explain  it's along the lines of 1/x = 0 being a limit that you approach, while .9 repeated is just notation for a rational number that you aren't approaching, you're already at (the value of which you can establish with algebra, as has been done earlier in the thread). i hope that makes sense  i'm currently buggered and in no state to really answer questions.
 damienthebloody
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as in a reciprocal function, where the line doesn't actually reach x=0, but just gets infinitely close. which i figure is the same as 0.99...=1Hawknc wrote:Well, he said f(x) = 1/x and x = 0, maybe I interpreted it wrong.
Peshmerga wrote:A blow job would probably get you a LOT of cheeseburgers.
But I digress.
 damienthebloody
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1/x as x approaches zero doesn't work in the same way, I think, because infinity is not a number. It's value gets arbitrarily large as x gets small, but there is still an infinitely large distance between f(small) and infinity.
0.999... is just the sum of a geometric series.
where the nth term is .9 / 10 ^ n
where n goes from n to infinity
or in sigma notation:
0.999... is just the sum of a geometric series.
where the nth term is .9 / 10 ^ n
where n goes from n to infinity
or in sigma notation:
Code: Select all
infinity

\ .9
\ 
/ n
/ 10

n = 0
There's an art to cooking toast
Never try to guess
Cook it till it's smoking
Then twenty seconds less.
Never try to guess
Cook it till it's smoking
Then twenty seconds less.
0.999... could be defined as the limit of 11/10^x as x approaches infinity. If we then say y=10^x (which allows for y> infinity as x> infinity), we can even declare that 0.999 is equal to the limit of 11/y. We know 1/y approaches zero as y approaches infinity, so 0.999=10=1.
I don't think I've seen that description before, and I think it's actually more convincing than most of the others.
I don't think I've seen that description before, and I think it's actually more convincing than most of the others.
LilyoftheShadow wrote:I believe this has a connection to the eternal distance halving.
At some point, it's close enough that it honestly dosen't matter anymore, but people will continue to pick it apart, ne?
No.
You're talking about 1/(2^x) as (integer) x becomes very large. It is never equal to zero. It does become "quite small" in some sense (but small compared to what?) and a physicist might call it negligible, but a mathmatician would not say it was ever equal to zero.
However, the limit of 1/(2^x) as x goes towards infinity is _exactly_ equal to zero.
The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
 damienthebloody
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SpitValve wrote:LilyoftheShadow wrote:I believe this has a connection to the eternal distance halving.
At some point, it's close enough that it honestly dosen't matter anymore, but people will continue to pick it apart, ne?
No.
You're talking about 1/(2^x) as (integer) x becomes very large. It is never equal to zero. It does become "quite small" in some sense (but small compared to what?) and a physicist might call it negligible, but a mathmatician would not say it was ever equal to zero.
However, the limit of 1/(2^x) as x goes towards infinity is _exactly_ equal to zero.
The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
those were exactly the words i was looking for last night.
 German Sausage
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 Akira
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SpitValve wrote:LilyoftheShadow wrote:I believe this has a connection to the eternal distance halving.
At some point, it's close enough that it honestly dosen't matter anymore, but people will continue to pick it apart, ne?
No.
You're talking about 1/(2^x) as (integer) x becomes very large. It is never equal to zero. It does become "quite small" in some sense (but small compared to what?) and a physicist might call it negligible, but a mathmatician would not say it was ever equal to zero.
However, the limit of 1/(2^x) as x goes towards infinity is _exactly_ equal to zero.
The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
Yup. You lost me.
Now leave my basic highschoolmath brain alone.
Lol.
LilyoftheShadow wrote:SpitValve wrote:LilyoftheShadow wrote:I believe this has a connection to the eternal distance halving.
At some point, it's close enough that it honestly dosen't matter anymore, but people will continue to pick it apart, ne?
No.
You're talking about 1/(2^x) as (integer) x becomes very large. It is never equal to zero. It does become "quite small" in some sense (but small compared to what?) and a physicist might call it negligible, but a mathmatician would not say it was ever equal to zero.
However, the limit of 1/(2^x) as x goes towards infinity is _exactly_ equal to zero.
The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
Yup. You lost me.
Now leave my basic highschoolmath brain alone.
Lol.
Basically, the infinite half step is solved and explained through calculus.
i hurd u liek mudkips???
 Akira
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Peshmerga wrote:LilyoftheShadow wrote:SpitValve wrote:LilyoftheShadow wrote:I believe this has a connection to the eternal distance halving.
At some point, it's close enough that it honestly dosen't matter anymore, but people will continue to pick it apart, ne?
No.
You're talking about 1/(2^x) as (integer) x becomes very large. It is never equal to zero. It does become "quite small" in some sense (but small compared to what?) and a physicist might call it negligible, but a mathmatician would not say it was ever equal to zero.
However, the limit of 1/(2^x) as x goes towards infinity is _exactly_ equal to zero.
The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
Yup. You lost me.
Now leave my basic highschoolmath brain alone.
Lol.
Basically, the infinite half step is solved and explained through calculus.
Evidently. O_o; *opted out of precalc* I only made it to AlgIII before I said "no more, I beg of you!"
Numbers aren't my thing, I'll admit up front. Lol
Re:
Oort wrote:However, I have doubts about the airplane one. If it matched the speed of the wheels, the plane would not move relative to the atmosphere, which is the important part.
Sure it would. If the treadmill were fast enough and long enough and wide enough. You don't even need the engine to be running. Due to the noslip condition, a layer of air would be pulled along by the treadmill's surface. Since the plane has inertia and lowfriction wheels, it would remain in the same spot while the air moving past it accelerates faster. Then the plane would take off, but it couldn't go anywhere, since the air velocity drops off as you move away from the surface. Eventually it would crash, but it could still take off.
 Mister_Penguin
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Re: The Truth
For kicks and giggles, I looked up the wikipedia page on Zeno's paradox.
After reading the talk page, I have an intense urge to punch someone in the genitals.
After reading the talk page, I have an intense urge to punch someone in the genitals.
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Re:
Holy necrobump Batman?
While we're here, though, I'd like to point out that...
...this was highly enlightening. I kept trying to imagine .9999... as an actual number, but defining it as a limit and not the precise decimal value makes it a lot clearer.
While we're here, though, I'd like to point out that...
SpitValve wrote:The limit is the value that the sequence or series approaches but never actually reaches. Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
...this was highly enlightening. I kept trying to imagine .9999... as an actual number, but defining it as a limit and not the precise decimal value makes it a lot clearer.
Insert witty phrase here.
 the_bandersnatch
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Re:
SpitValve wrote:Numbers such as 0.999... are not defined as any particular value in the series  instead they're defined as the _limit_ of the series, and that's why they have exact values, e.g. 0.999...=1.
I see what you're saying here, and it makes sense in a way, why should we define a number as the limit of the series and not the exact value? I thought maths was all about defining exact values?
And I've spotted what I believe to be a flaw in the reasoning on that website that was linked (http://qntm.org/?pointnine):
"But 0.0000... should have a 1 at the end!"
No, it shouldn't. "0.0000...1" is meaningless. The "..." means the zeros go on forever. "Forever" means "without end". There IS no end for the final 1 to go on.
It seems to me here he's just changed the goalposts  he might be correct in saying that in the real world "there is no end for the final one to go on", but in maths we can still refer to the infinite sequence of zeroes between the decimal point and the final digit and then do stuff with it. To me, that's one of the fundamental ways mathematics works. We could even assign that infinite sequence of zeroes a notational symbol and work from there. (As an example, in the real world the square root of 1 does not exist, but we can still assign it a symbol within the framework of our mathematics and go from there).
In girum imus nocte, et consumimur igni
Re: The Truth
But you're trying to redefine an 'infinitely long string of something' as something else.
Whereas relabeling sqrt(1) as an algebraic quantity is just the same as "Let x = 1"
Sure, there's a whole subset of maths based on it, but it's not the same.
And how much can you really do to an infinitely long string of zero's without changing its' value?
Out of interests sake, the "One at the end of the zero's" argument I like to refute with:
"You have an infinitely long piece of string. I tied a knot at the end of it. Took a while to get back."
Whereas relabeling sqrt(1) as an algebraic quantity is just the same as "Let x = 1"
Sure, there's a whole subset of maths based on it, but it's not the same.
And how much can you really do to an infinitely long string of zero's without changing its' value?
Out of interests sake, the "One at the end of the zero's" argument I like to refute with:
"You have an infinitely long piece of string. I tied a knot at the end of it. Took a while to get back."
Why is it that 4chan is either infinitely awesome, infinitely bad, or "lolwut", but never any intermediary level?
 arcticfox.sq
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Re: The Truth
The plane would take off because how fast it goes and whether it moves at all does not depend on the wheels. A PLANE IS NOT THE SAME AS A BIG CAR WITH WINGS. They go because the engines power the fans (in the wings). Thus no matter what is under it it will move, that is, unless the wheels are so full of friction it takes more power than the engines can provide to lift it. So no power (or very very little, I'm not sure about the detailed workings) goes towards turning the wheels, the wheels only turn because the engine is pulling the wings forwards, thus pulling the plane forwards. Add a treadmill and all you have is the wheels turning at the speed of the plane relative to the ground plus the speed of treadmill relative to the ground. The speed of the plane would not be affected at all (except that the wheels aren't perfectly frictionless, so it slows down a tiny amount).
Also, Believe it or Not did this with a giant taupe pulled by a truck. It worked. Science wins.
Edited for silly
Also, Believe it or Not did this with a giant taupe pulled by a truck. It worked. Science wins.
Edited for silly
Last edited by arcticfox.sq on Fri Apr 25, 2008 5:07 am UTC, edited 1 time in total.
 Hawknc
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Re: The Truth
It's that time again already?
 the_bandersnatch
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Re: The Truth
Hawknc wrote:It's that time again already?
Yes. Yes it is.
In girum imus nocte, et consumimur igni
Re: The Truth
arcticfox.sq wrote:The plane would not take off...
This line and the rest of your post are completely at odds at one another, so either you're joking or the 'not' was a mistake.
Why is it that 4chan is either infinitely awesome, infinitely bad, or "lolwut", but never any intermediary level?
 Hawknc
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Re: The Truth
I don't really want to get into this argument again, but arcticfox's argument seems consistent with the conclusion that the aircraft won't take off.
Re: The Truth
Thus no matter what is under it it will move
The speed of the plane would not be affected at all
Both these lines show the plane moving forward, and this forward momentum means the plane will take off.
Why is it that 4chan is either infinitely awesome, infinitely bad, or "lolwut", but never any intermediary level?
 SecondTalon
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Re: The Truth
Goddamn it, they did it on Mythbusters. Are two special effects Jesters performing tricks for you not good enough?
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heuristically_alone wrote:I have been informed that this is called writing a book.
Re: The Truth
arcticfox.sq wrote:The plane would not take off because how fast it goes and whether it moves at all does not depend on the wheels. A PLANE IS NOT THE SAME AS A BIG CAR WITH WINGS. They go because the engines power the fans (in the wings).
And thus, the plane would take off.
But even without an engine, the plane could still take off if the wheels were frictionless enough and the conveyor belt had a huge surface area and started very quickly, due to the boundary layer and the noslip condition.

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Re: The Truth
I thought about the plane on the treadmill situation as follows:
Given the most simplistic model of it then the hinging factor is the friction within the wheel bearings. Disregarding the point at which tires don't make contact with the surface and assuming they don't skid, as well as perfect integrity among every component... the bearings are the only place where the 2 forces (From the engines and the treadmill) directly interact. In an interpretation, you could assume the question is closer to whether the treadmill can or cannot stop a plane taking off.
Then the answer would be: If there is friction, there will always be a speed (Given were not limited by speed of light in this model) at which the treadmill can run to cause the plane to be relatively motionless. If there is no friction, then there will never be a speed at which the treadmill can run to stop the plane taking off.
If it were taken with the interpretation that the treadmill would match the same speed, then it depends on the force that the engines are able to produce relative to the friction in the bearings. It's kind of complicated since the model brings in the concept of infinite power, especially when both forces are considered infinitely powerful. Then essentially you're boiling down to the difference between infinity and infinity multiplied by the effect of the bearings, which doesn't make sense.
Given another model of simply you pushing a cube across a desk. If you started out pushing the block at 1m/s, if somehow the friction steadily increased, eventually you wouldn't be strong enough to overcome the force.
The level of ambiguity in the question doesn't help. I'm sure if it were put in a simple model it would be easy. Also my pisspoor explanation an analogies of what I was thinking doesn't help. I really do suck at explaining my ideas all that well.
1/0 = Undefined. Just because it's simple and just because you can use standard notation doesn't mean its meaningful.
0.999 reoccurring = 1. Just because the symbols are different, doesn't mean it can't denote the same concept and just because it uses symbols which would individually imply that it can't be the same, doesn't mean as a whole it is the same.
Given the most simplistic model of it then the hinging factor is the friction within the wheel bearings. Disregarding the point at which tires don't make contact with the surface and assuming they don't skid, as well as perfect integrity among every component... the bearings are the only place where the 2 forces (From the engines and the treadmill) directly interact. In an interpretation, you could assume the question is closer to whether the treadmill can or cannot stop a plane taking off.
Then the answer would be: If there is friction, there will always be a speed (Given were not limited by speed of light in this model) at which the treadmill can run to cause the plane to be relatively motionless. If there is no friction, then there will never be a speed at which the treadmill can run to stop the plane taking off.
If it were taken with the interpretation that the treadmill would match the same speed, then it depends on the force that the engines are able to produce relative to the friction in the bearings. It's kind of complicated since the model brings in the concept of infinite power, especially when both forces are considered infinitely powerful. Then essentially you're boiling down to the difference between infinity and infinity multiplied by the effect of the bearings, which doesn't make sense.
Given another model of simply you pushing a cube across a desk. If you started out pushing the block at 1m/s, if somehow the friction steadily increased, eventually you wouldn't be strong enough to overcome the force.
The level of ambiguity in the question doesn't help. I'm sure if it were put in a simple model it would be easy. Also my pisspoor explanation an analogies of what I was thinking doesn't help. I really do suck at explaining my ideas all that well.
1/0 = Undefined. Just because it's simple and just because you can use standard notation doesn't mean its meaningful.
0.999 reoccurring = 1. Just because the symbols are different, doesn't mean it can't denote the same concept and just because it uses symbols which would individually imply that it can't be the same, doesn't mean as a whole it is the same.
 arcticfox.sq
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Re:
Andrew wrote:Verysillyman wrote:Owijad wrote:Various other issues aside, that only applies to girls. An attractive guy cannot be nearly as promiscuous as an attractive girl.
I want to disprove that.
Unless the girls in question are lesbians I think it's by definition untrue. (If you ignore the slight imbalance in gender across the population.)
The means have to be the same (assuming equal populations), but the most promiscuous don't have to be the same.
Re: The Truth
Wasn't this thread created precisely to avoid the current one?
This is a placeholder until I think of something more creative to put here.
Re:
fjafjan wrote:you should read the god delusion, it turned me into truly atheist...
Funny that. It had the exact opposite effect on me  I concluded there must be a God because I couldn't bear to live in a universe where Richard Dawkins would be right.
I started out the book keeping count of the known dodgy rhetorical tricks, logic errors and standard fallacies and gave up before completing the first page of the introduction  I forget what the count was at that point, but it was more than 3...
Some years ago, I saw a TV program where Richard Dawkins was put in a room with a fanatical fundamentalist Christian of some description. You had to pay close attention to the content of their dialogue to tell the two apart.
Seriously, while the arguments of a fundamentalist atheist like Dawkins are great at helping existing confirmed atheists feel smug, I'd no more suggest using them to try to convince a nonatheist that there is no God than I'd suggest using Chick Tracts to convince a penandpaper roleplayer than D&D is the recruitment tool of satanism, or getting Jack Thompson to convince someone that playing video games sends people on reallife killing sprees...
Re: The Truth
.................
Last edited by Daimon on Thu Dec 06, 2012 6:48 pm UTC, edited 1 time in total.
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