Mathematics of Insanity - Tilted Forum Project Discussion Community

Slims · 06-26-2003, 05:23 PM

You have an infinite number of marbles numbered sequentially 1,2,3, etc. and a bag to hold them all.

Problem 1:
If you put the marbles in the bag, ten at a rate of ten marbles per second, sequentially (marbles 1-10 first, 11-20 second, etc.), and you remove the marbles at a rate of 1 per second, sequentially (I.e. 1,2,3, etc.), how many marbles are in the bag as time goes to infinity?

Problem 2: Same as 1, except you remove the marbles by pulling out every tenth marble (i.e. you remove number 10, 20, 30, etc.) , as time goes to infinity, how many marbles are in the bag?

Hint: The answers are not the same.

It was a problem like this one that drove (I think I have the right mathematician) the russian mathematician Cantor crazy.

have fun.

Please feel free to post your answers/proofs.

CSflim · 06-27-2003, 11:46 AM

Any problems that involve infinity in this manner are not really solvable.

The obvious answer to both of them would be that at the end, the bag contains 9/10 of inifinty, i.e infinity.

However if you look at question 1, you could regard it in this way:
All marbles are going to be put in the bag evenentually....alll marbles are going to come out of the bag, eventually, so the answer could be 0.

Sleepyjack · 06-28-2003, 05:22 AM

hmm i haven't done calculus for a while but isn't this a basic limits of infinite sequences or series?

ie sequence a is something like = 10n - n
the sequence b is something like = 10n-n as well ??? although for the first sequence you basically put 10 marbles in and take one out every second, and then in the second you put 10 in, although the rate at pulling out every tenth marble is not specified?

the way i have defined it, the 2 series converge or approach to infinity as n approaches infinity, ie the equations both equal 9n, the same as CSflim.

you say the answers are different how do you know?

also excuse my calc if it is a bit off, i haven't done it for a while...

Eviltree · 07-01-2003, 09:41 PM

my brraaaiinnn! BANG!

MacGnG · 07-01-2003, 11:03 PM

they arent going to be the same number, but as you get closer to infinity, the difference in the number of marbles in each bag becomes negligible.

it might be a significant difference when you are around conceivable numbers but as you get closer to infinity 100,000 is insignificant in the grand scheme of the thing.

If you use scientific notation, for whatever reason, round to the thousandths place (*arbitrary digit* say 3rd decimal), so 1234567890 =1.234*10^9 . when you get upto like 10^10000000000000000000 , 5milliion is like half a penny.

sure its not a real answer but i dont remember how to do that math (ITS SUMMER)

Slims · 07-01-2003, 11:22 PM

With the first problem, ever marble that goes into the bag, eventually comes out. So when time goes to infinity, you will eventually take out every single marble, thus there will be no marbles in the bag.

With the second problem, you only remove certain marbles, and an infinite number of particular marbles (like number 2,3,4,22, etc.) will always be in the bag, thus when time goes to infinity, there will be an infinite number of marbles in the bag.

Sleepyjack · 07-02-2003, 12:59 AM

ok, so the tenth marble always has to be a multiple of 10?
like 10,20,30 etc
i just thought it's every tenth marble and it doens't matter which number it was, hence it is the same as problem 1, in that you take out a marble after putting in 10, wether its the tenth or not. I see the difference now. i think?

One thing is that for there to be no marbles in the bag, the out rate has to exceed (at a point of time) or go for a longer period of time, than the in rate. Which i am having trouble coming to terms with???

Slims · 07-02-2003, 01:01 AM

Yes, pretend that every marble has a number etched on it.

And yes, the rate of marbles entering the bag is greater than the rate of marbles leaving the bag.

This problem was used an analysis class to demonstrate some of the more mind boggling things that can happen when you introduce infinities.

Sleepyjack · 07-02-2003, 01:21 AM

yes mind boggling!

however, i still can't get over the fact that the in rate is always greater than the rate out... so how can all the marbles come out??

Slims · 07-02-2003, 01:32 AM

[QUOTE]Originally posted by Sleepyjack
yes mind boggling!

however, i still can't get over the fact that the in rate is always greater than the rate out... so how can all the marbles come out?? [/QUOTE

With the first problem they all come out because you are removing an infinite number of marbles sequentially. You can name any number, and I would be able to pick it up from the discard pile and show you that it had been removed, therefore there are no marbles in the bag.

Sleepyjack · 07-02-2003, 03:25 AM

yeah i understand that, ie that you'll eventually remove all marbles sequentially and then the other case you only take out the mulitples of ten.
i guess the in and out rate are of no consequence really, given we're dealing with the idea of infinity, its just the manner in which you take the marbles out which matters.

cool, i think i get it now....

CSflim · 07-02-2003, 09:16 AM

Quote:

Originally posted by Greg700
With the first problem, ever marble that goes into the bag, eventually comes out. So when time goes to infinity, you will eventually take out every single marble, thus there will be no marbles in the bag.

With the second problem, you only remove certain marbles, and an infinite number of particular marbles (like number 2,3,4,22, etc.) will always be in the bag, thus when time goes to infinity, there will be an infinite number of marbles in the bag.

Wohoo! I was right! Go me! I kick ass! In your face space coyote!

mtsgsd · 07-02-2003, 10:47 AM

I'm struggling to wrap my mind around your answer greg700.

in the first problem each marble eventualy comes out of the bag yes. BUT for every marble removed, 10 are placed inside. Since the set of marbles is infinite, I would think that you would never be able to empty the bag.

I see the second problem as identical to the first? every 10 marble is in effect the same as the sequential method. You still have 1 coming out every second while 10 are going in. True, this gaurantees that marbles will be left in the bag if the process is terminated before infinity, but see my point above.

Seems to me that you would have a shitload of marbles in the bag either way, with no way to calculate the number because it goes on infinately.

Ok, so what am I missing besides my brains?

Slims · 07-02-2003, 11:51 AM

When my professor first gave us this problem, I raised a big stink in class and insisted that there were an infinite number of marbles in each bag.

Apparently I am wrong, and I don't completely understand why. Intuitively it makes sense that if you are putting more marbles into a bag than you are removing, then you will always have marbles in the bag, but mathematicaly this doesn't work.

I think the problem has to do with the difference between 'on the way to infinity' and 'at infinity'

If you stop at any finite time, there will be a lot of marbles in the bag, and as time increases, the number of marbles in the bag will increase. However, at time equals infinity, all the marbles in the bag (in problem 1) will have been removed, so the total number of marbles will be 0.

Even though we can find the answer to problems like this one mathematically, I don't think they will ever completely make sense.

this problem was supposed to be a nice introduciton to the wierdness that is cantor sets, and they are even worse.

Oh, and good job CSflim, I didn't want to congratulate you before a discussion got underway.

mtsgsd · 07-02-2003, 12:05 PM

Interesting. Just for the sake of discussion, not argument...

We seem to be treating "at infinity" as a finite number, as though it can be reached. Ok, then at infinity we will have naturaly used up our supply of marbles ten times faster than it took to reach infinity, therefore the supply ran out long before we finished taking them out. Having an infinite supply of seconds, we can therefore remove the inifinite number of balls.

I get it, but I don't agree with the argument as it implies that we would run out of marbles in a finite time. We can't calculate it, but eventually we would have to run out of marbles before time ran out, even though the number is infinite.

Arguments? I hope I'm not making an ass of myself. I love this kind of problem.

CSflim · 07-02-2003, 12:24 PM

Quote:

Originally posted by mtsgsd
Interesting. Just for the sake of discussion, not argument...

We seem to be treating "at infinity" as a finite number, as though it can be reached. Ok, then at infinity we will have naturaly used up our supply of marbles ten times faster than it took to reach infinity, therefore the supply ran out long before we finished taking them out. Having an infinite supply of seconds, we can therefore remove the inifinite number of balls.

I get it, but I don't agree with the argument as it implies that we would run out of marbles in a finite time. We can't calculate it, but eventually we would have to run out of marbles before time ran out, even though the number is infinite.

Arguments? I hope I'm not making an ass of myself. I love this kind of problem.

Does infinity even exist?
http://www.tfproject.org/tfp/showthr...threadid=13340

read my post there for my take on this issue.

Slims · 07-02-2003, 12:37 PM

I am not treating infinity as a finite number. And I am not ever assuming we ran out of marbles, even though we may have lost some.

Think about this:

Take the equation y=(1-x)/(1-x)

In this case, the limit as x->1 exists and is 1, but the value of y is undefined at x=1 (0/0).

This is one of the easiest ways I can express the difference between approaching a value, and actually reaching it.

Bear in mind that I am no expert, and I am trying to illustrate a much more subtle problem with simple examples (between beers).

sportsrule101 · 07-03-2003, 04:10 AM

Its not the best written math problem, because time never goes to infinity(its never been proven). Surprised the teacher used it, most try to stay with just math and other analytical theories and stay away from philosophy.

rodimus · 07-06-2003, 08:00 PM

damnit. i thought i was done with calc when i left my calc 3 class for vacation, but nooooo. it's here on this damn board too. lol

Zargix · 07-07-2003, 08:23 PM

this reminds me of something else kinda interesting, in the form of one of those silly word problems in text books.

A goat herder has this field, that is in infininte amount of acres big. He also has an infinite amount of goats. If he uses his magical goatherding powers to evenly distrubute the goats among the field, how many goats are there per acre.

1 goat per acre?

yeah the same problem, is any part of infinity still infinity? hmmm.. 1/10 of infinity = infinity. Doesn't make much sense. the only other number that somethine like that works for is zero, such as 1/10 of zero is still zero. I tend to like to think that infinity divided by zero is one, but thats just me.

I'm so sorry about this post, I'm tired! I can't help it! I just love these kinds of problems, even if I'm so barely awake I can hardly read it.

just my $.02

bermuDa · 07-07-2003, 09:13 PM

if it takes an infinite amount of time to put an infinite number of marbles in the bag, then you never have a chance to remove any marbles... so the answer is an infinite amount of marbles

we can't reach the end of the problem, since the number of marbles in the bag is always increasing.

elian gonsalez · 07-07-2003, 10:48 PM

i have a question, if you can graph the increase of the marbles, using straight lines, which are infinite, and continue forever, wouldnt that disprove your answer?

bermuDa · 07-08-2003, 04:47 PM

greg: could your ask your teacher about my answer? If the problem starts off with putting an infinite number of marbles in a bag one by one.... wouldn't that mean you'd be putting marbles in the bag for eternity and never have a chance to remove any of them?

Slims · 07-09-2003, 07:22 AM

Bermuda: Yep, that would make a huge difference, because you could never run out of marbles.

This problem is similar to the problems that drove a brilliant mathematician to repeated nervous breakdowns and insanity.

It doesn't really make sense. It's just mindfuck really, but it works out mathematically.

If you guys want, I can probably write a small proof, or I can ask my teacher next semester to do it for me, since he really knows what he is talking about.

Sleepyjack · 07-09-2003, 08:04 AM

on a side note, what do you actually study Greg700?

Slims · 07-09-2003, 12:24 PM

I am an ex spanish then geology major, and now I am on an applied math kick with a smattering of physics.

niek · 07-10-2003, 01:33 AM

You just can't create mathematical problems with infinity, infinity cannot be added to an equation; in both problems A and B you substract from infinity, you juste can't do that.

OK, let's suppose you forgot and this is a totally HYPOTHETICAL problem:

-Problem A; infinity-infinity then you would amount to 0

-Prblem B; infinity*9/10 then you would still amount to infinity

asaris · 07-10-2003, 05:49 AM

Quote:

Originally posted by niek

-Problem A; infinity-infinity then you would amount to 0

-Prblem B; infinity*9/10 then you would still amount to infinity

But infinity-infinity isn't necessarily 0. Take the natural numbers. Subtract all the even numbers. Still have an infinite set.

What Greg700 is saying is that, in the first case, for every marble x, as t goes to infinity, x will have been removed from the bag. But in the second case, this doesn't hold -- it only hold for those marbles such that x=10n. So there's an infinite number of marbles.

duckznutz · 07-10-2003, 01:20 PM

This is all nonsense Greg 700 . . . . . the experiment has no 'end' therefore you cannot 'stop' to count your marbles . .all you can do is take a snapshot view at any given time . . . .

Condition 1 - At any given time there are 9 times as many marbles IN the bag as ot of it. You will never take them all out because you are always putting them in at a rate of 9 to 1. the bag jsut gets bigger ad infinitum.

Condition 2 - Exactly the same except there are always 9 more marbles in the bag after any given amount of time has elapsed (assuming you removed marble 1 in Condition 1 immediately upon putting it in).

duckznutz · 07-10-2003, 01:22 PM

"As time goes to infinity"? An abstract concept if ever there was one . . . . you cannot put a figure on that. WHEN does time 'go to infinity?'

duckznutz · 07-10-2003, 01:24 PM

I dont think you can 'mix' the real world of marbles and bags with the conceptual world of mathematics . . . that is why you are getting yourself all confused.

duckznutz · 07-10-2003, 01:31 PM

you are attempting to 'transfer' the abstract concept that is numbers into reality by imagining numbers on marbles. You are effectively attempting to 'humanise' the numbers and give them 'life' by saying that they are no longer an abstract concept but are in fact small glass spheres. Now that is fine BUT as time goes to infinity then the bag grows to infinity . . . . . . . a bag of marbles infinitely would be VERY big relative to the little bag we can all easily imagine we started with . . . . your humanisation of the abstract theory is then lost as we all struggle to imagine an infinitly big bag of marbles . . . . . . . . . our brains cannot cope and so BANG!

bermuDa · 07-10-2003, 05:29 PM

you should try the edit button, it cuts down on the ridiculous amounts of consecutive posts.

debaser · 07-10-2003, 07:01 PM

The answer above was incorrect. In both cases there will be an infinite number of marbels inside the bag and outside the bag.

In the first case the marbels outside the bag will be sequentially numbered, in the second case they will be numbered by tens.

Simple really.

duckznutz · 07-11-2003, 12:51 AM

Quote:

Originally posted by bermuDa
you should try the edit button, it cuts down on the ridiculous amounts of consecutive posts.

Sorry folks . . never occurred that I could do that. Point taken bermuDa.

bermuDa · 07-11-2003, 01:10 AM

just here to help

you made some good points in those posts

TIO · 07-11-2003, 01:29 AM

Debaser has it right. Sure, you can name any number, and show me that that number is no longer in the bag, but I can always name a number that is still in the bag.

duckznutz · 07-11-2003, 05:16 AM

Thanks bermuDa . . no-one is immune to flattery! Did I mention that I think you are a wonderful person!

06-26-2003, 05:23 PM	#1 (permalink)
Slims Eccentric insomniac Location: North Carolina	Mathematics of Insanity You have an infinite number of marbles numbered sequentially 1,2,3, etc. and a bag to hold them all. Problem 1: If you put the marbles in the bag, ten at a rate of ten marbles per second, sequentially (marbles 1-10 first, 11-20 second, etc.), and you remove the marbles at a rate of 1 per second, sequentially (I.e. 1,2,3, etc.), how many marbles are in the bag as time goes to infinity? Problem 2: Same as 1, except you remove the marbles by pulling out every tenth marble (i.e. you remove number 10, 20, 30, etc.) , as time goes to infinity, how many marbles are in the bag? Hint: The answers are not the same. It was a problem like this one that drove (I think I have the right mathematician) the russian mathematician Cantor crazy. have fun. Please feel free to post your answers/proofs.

06-27-2003, 11:46 AM	#2 (permalink)
CSflim Sky Piercer Location: Ireland	Any problems that involve infinity in this manner are not really solvable. The obvious answer to both of them would be that at the end, the bag contains 9/10 of inifinty, i.e infinity. However if you look at question 1, you could regard it in this way: All marbles are going to be put in the bag evenentually....alll marbles are going to come out of the bag, eventually, so the answer could be 0. __________________

07-01-2003, 11:22 PM	#6 (permalink)
Slims Eccentric insomniac Location: North Carolina	With the first problem, ever marble that goes into the bag, eventually comes out. So when time goes to infinity, you will eventually take out every single marble, thus there will be no marbles in the bag. With the second problem, you only remove certain marbles, and an infinite number of particular marbles (like number 2,3,4,22, etc.) will always be in the bag, thus when time goes to infinity, there will be an infinite number of marbles in the bag. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-02-2003, 01:01 AM	#8 (permalink)
Slims Eccentric insomniac Location: North Carolina	Yes, pretend that every marble has a number etched on it. And yes, the rate of marbles entering the bag is greater than the rate of marbles leaving the bag. This problem was used an analysis class to demonstrate some of the more mind boggling things that can happen when you introduce infinities. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-02-2003, 01:32 AM	#10 (permalink)
Slims Eccentric insomniac Location: North Carolina	[QUOTE]Originally posted by Sleepyjack yes mind boggling! however, i still can't get over the fact that the in rate is always greater than the rate out... so how can all the marbles come out?? [/QUOTE With the first problem they all come out because you are removing an infinite number of marbles sequentially. You can name any number, and I would be able to pick it up from the discard pile and show you that it had been removed, therefore there are no marbles in the bag. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

06-28-2003, 05:22 AM	#3 (permalink)
Sleepyjack Fast'n'Bulbous Location: Australia, Perth	hmm i haven't done calculus for a while but isn't this a basic limits of infinite sequences or series? ie sequence a is something like = 10n - n the sequence b is something like = 10n-n as well ??? although for the first sequence you basically put 10 marbles in and take one out every second, and then in the second you put 10 in, although the rate at pulling out every tenth marble is not specified? the way i have defined it, the 2 series converge or approach to infinity as n approaches infinity, ie the equations both equal 9n, the same as CSflim. you say the answers are different how do you know? also excuse my calc if it is a bit off, i haven't done it for a while...

07-01-2003, 09:41 PM	#4 (permalink)
Eviltree Psycho Location: British Columbia	my brraaaiinnn! BANG!

07-01-2003, 11:03 PM	#5 (permalink)
MacGnG Know Where!	they arent going to be the same number, but as you get closer to infinity, the difference in the number of marbles in each bag becomes negligible. it might be a significant difference when you are around conceivable numbers but as you get closer to infinity 100,000 is insignificant in the grand scheme of the thing. If you use scientific notation, for whatever reason, round to the thousandths place (arbitrary digit say 3rd decimal), so 1234567890 =1.234*10^9 . when you get upto like 10^10000000000000000000 , 5milliion is like half a penny. sure its not a real answer but i dont remember how to do that math (ITS SUMMER)

07-02-2003, 12:59 AM	#7 (permalink)
Sleepyjack Fast'n'Bulbous Location: Australia, Perth	ok, so the tenth marble always has to be a multiple of 10? like 10,20,30 etc i just thought it's every tenth marble and it doens't matter which number it was, hence it is the same as problem 1, in that you take out a marble after putting in 10, wether its the tenth or not. I see the difference now. i think? One thing is that for there to be no marbles in the bag, the out rate has to exceed (at a point of time) or go for a longer period of time, than the in rate. Which i am having trouble coming to terms with???

07-02-2003, 01:21 AM	#9 (permalink)
Sleepyjack Fast'n'Bulbous Location: Australia, Perth	yes mind boggling! however, i still can't get over the fact that the in rate is always greater than the rate out... so how can all the marbles come out??

07-02-2003, 03:25 AM	#11 (permalink)
Sleepyjack Fast'n'Bulbous Location: Australia, Perth	yeah i understand that, ie that you'll eventually remove all marbles sequentially and then the other case you only take out the mulitples of ten. i guess the in and out rate are of no consequence really, given we're dealing with the idea of infinity, its just the manner in which you take the marbles out which matters. cool, i think i get it now....

07-02-2003, 10:47 AM	#13 (permalink)
mtsgsd Addict Location: Wisconsin, USA	I'm struggling to wrap my mind around your answer greg700. in the first problem each marble eventualy comes out of the bag yes. BUT for every marble removed, 10 are placed inside. Since the set of marbles is infinite, I would think that you would never be able to empty the bag. I see the second problem as identical to the first? every 10 marble is in effect the same as the sequential method. You still have 1 coming out every second while 10 are going in. True, this gaurantees that marbles will be left in the bag if the process is terminated before infinity, but see my point above. Seems to me that you would have a shitload of marbles in the bag either way, with no way to calculate the number because it goes on infinately. Ok, so what am I missing besides my brains?

07-02-2003, 11:51 AM	#14 (permalink)
Slims Eccentric insomniac Location: North Carolina	When my professor first gave us this problem, I raised a big stink in class and insisted that there were an infinite number of marbles in each bag. Apparently I am wrong, and I don't completely understand why. Intuitively it makes sense that if you are putting more marbles into a bag than you are removing, then you will always have marbles in the bag, but mathematicaly this doesn't work. I think the problem has to do with the difference between 'on the way to infinity' and 'at infinity' If you stop at any finite time, there will be a lot of marbles in the bag, and as time increases, the number of marbles in the bag will increase. However, at time equals infinity, all the marbles in the bag (in problem 1) will have been removed, so the total number of marbles will be 0. Even though we can find the answer to problems like this one mathematically, I don't think they will ever completely make sense. this problem was supposed to be a nice introduciton to the wierdness that is cantor sets, and they are even worse. Oh, and good job CSflim, I didn't want to congratulate you before a discussion got underway. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-02-2003, 12:05 PM	#15 (permalink)
mtsgsd Addict Location: Wisconsin, USA	Interesting. Just for the sake of discussion, not argument... We seem to be treating "at infinity" as a finite number, as though it can be reached. Ok, then at infinity we will have naturaly used up our supply of marbles ten times faster than it took to reach infinity, therefore the supply ran out long before we finished taking them out. Having an infinite supply of seconds, we can therefore remove the inifinite number of balls. I get it, but I don't agree with the argument as it implies that we would run out of marbles in a finite time. We can't calculate it, but eventually we would have to run out of marbles before time ran out, even though the number is infinite. Arguments? I hope I'm not making an ass of myself. I love this kind of problem.

07-02-2003, 12:37 PM	#17 (permalink)
Slims Eccentric insomniac Location: North Carolina	I am not treating infinity as a finite number. And I am not ever assuming we ran out of marbles, even though we may have lost some. Think about this: Take the equation y=(1-x)/(1-x) In this case, the limit as x->1 exists and is 1, but the value of y is undefined at x=1 (0/0). This is one of the easiest ways I can express the difference between approaching a value, and actually reaching it. Bear in mind that I am no expert, and I am trying to illustrate a much more subtle problem with simple examples (between beers). __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-03-2003, 04:10 AM	#18 (permalink)
sportsrule101 Insane	Its not the best written math problem, because time never goes to infinity(its never been proven). Surprised the teacher used it, most try to stay with just math and other analytical theories and stay away from philosophy. __________________ winning isn't everything but losing isn't anything

07-06-2003, 08:00 PM	#19 (permalink)
rodimus Insane	damnit. i thought i was done with calc when i left my calc 3 class for vacation, but nooooo. it's here on this damn board too. lol

07-07-2003, 08:23 PM	#20 (permalink)
Zargix Crazy Location: Everywhere, Simultaniously	this reminds me of something else kinda interesting, in the form of one of those silly word problems in text books. A goat herder has this field, that is in infininte amount of acres big. He also has an infinite amount of goats. If he uses his magical goatherding powers to evenly distrubute the goats among the field, how many goats are there per acre. 1 goat per acre? yeah the same problem, is any part of infinity still infinity? hmmm.. 1/10 of infinity = infinity. Doesn't make much sense. the only other number that somethine like that works for is zero, such as 1/10 of zero is still zero. I tend to like to think that infinity divided by zero is one, but thats just me. I'm so sorry about this post, I'm tired! I can't help it! I just love these kinds of problems, even if I'm so barely awake I can hardly read it. just my $.02

07-07-2003, 09:13 PM	#21 (permalink)
bermuDa don't ignore this--> Location: CA	if it takes an infinite amount of time to put an infinite number of marbles in the bag, then you never have a chance to remove any marbles... so the answer is an infinite amount of marbles we can't reach the end of the problem, since the number of marbles in the bag is always increasing. __________________ I am the very model of a moderator gentleman.

07-07-2003, 10:48 PM	#22 (permalink)
elian gonsalez Upright	i have a question, if you can graph the increase of the marbles, using straight lines, which are infinite, and continue forever, wouldnt that disprove your answer?

07-08-2003, 04:47 PM	#23 (permalink)
bermuDa don't ignore this--> Location: CA	greg: could your ask your teacher about my answer? If the problem starts off with putting an infinite number of marbles in a bag one by one.... wouldn't that mean you'd be putting marbles in the bag for eternity and never have a chance to remove any of them? __________________ I am the very model of a moderator gentleman.

07-09-2003, 07:22 AM	#24 (permalink)
Slims Eccentric insomniac Location: North Carolina	Bermuda: Yep, that would make a huge difference, because you could never run out of marbles. This problem is similar to the problems that drove a brilliant mathematician to repeated nervous breakdowns and insanity. It doesn't really make sense. It's just mindfuck really, but it works out mathematically. If you guys want, I can probably write a small proof, or I can ask my teacher next semester to do it for me, since he really knows what he is talking about. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-09-2003, 08:04 AM	#25 (permalink)
Sleepyjack Fast'n'Bulbous Location: Australia, Perth	on a side note, what do you actually study Greg700?

07-09-2003, 12:24 PM	#26 (permalink)
Slims Eccentric insomniac Location: North Carolina	I am an ex spanish then geology major, and now I am on an applied math kick with a smattering of physics. __________________ "Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill "All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence

07-10-2003, 01:33 AM	#27 (permalink)
niek Banned	You just can't create mathematical problems with infinity, infinity cannot be added to an equation; in both problems A and B you substract from infinity, you juste can't do that. OK, let's suppose you forgot and this is a totally HYPOTHETICAL problem: -Problem A; infinity-infinity then you would amount to 0 -Prblem B; infinity*9/10 then you would still amount to infinity

07-10-2003, 01:20 PM	#29 (permalink)
duckznutz Addict Location: Brook Cottage, Lanark, Scotland	This is all nonsense Greg 700 . . . . . the experiment has no 'end' therefore you cannot 'stop' to count your marbles . .all you can do is take a snapshot view at any given time . . . . Condition 1 - At any given time there are 9 times as many marbles IN the bag as ot of it. You will never take them all out because you are always putting them in at a rate of 9 to 1. the bag jsut gets bigger ad infinitum. Condition 2 - Exactly the same except there are always 9 more marbles in the bag after any given amount of time has elapsed (assuming you removed marble 1 in Condition 1 immediately upon putting it in). __________________ Where your talents and the needs of the world cross . . there lies your vocation.

07-10-2003, 01:22 PM	#30 (permalink)
duckznutz Addict Location: Brook Cottage, Lanark, Scotland	"As time goes to infinity"? An abstract concept if ever there was one . . . . you cannot put a figure on that. WHEN does time 'go to infinity?' __________________ Where your talents and the needs of the world cross . . there lies your vocation.

07-10-2003, 01:24 PM	#31 (permalink)
duckznutz Addict Location: Brook Cottage, Lanark, Scotland	I dont think you can 'mix' the real world of marbles and bags with the conceptual world of mathematics . . . that is why you are getting yourself all confused. __________________ Where your talents and the needs of the world cross . . there lies your vocation.

07-10-2003, 01:31 PM	#32 (permalink)
duckznutz Addict Location: Brook Cottage, Lanark, Scotland	you are attempting to 'transfer' the abstract concept that is numbers into reality by imagining numbers on marbles. You are effectively attempting to 'humanise' the numbers and give them 'life' by saying that they are no longer an abstract concept but are in fact small glass spheres. Now that is fine BUT as time goes to infinity then the bag grows to infinity . . . . . . . a bag of marbles infinitely would be VERY big relative to the little bag we can all easily imagine we started with . . . . your humanisation of the abstract theory is then lost as we all struggle to imagine an infinitly big bag of marbles . . . . . . . . . our brains cannot cope and so BANG! __________________ Where your talents and the needs of the world cross . . there lies your vocation.

07-10-2003, 05:29 PM	#33 (permalink)
bermuDa don't ignore this--> Location: CA	you should try the edit button, it cuts down on the ridiculous amounts of consecutive posts. __________________ I am the very model of a moderator gentleman.

07-10-2003, 07:01 PM	#34 (permalink)
debaser Sir, I have a plan... Location: 38S NC20943324	The answer above was incorrect. In both cases there will be an infinite number of marbels inside the bag and outside the bag. In the first case the marbels outside the bag will be sequentially numbered, in the second case they will be numbered by tens. Simple really. __________________ Fortunato became immured to the sound of the trowel after a while.

07-11-2003, 01:10 AM	#36 (permalink)
bermuDa don't ignore this--> Location: CA	just here to help you made some good points in those posts __________________ I am the very model of a moderator gentleman.

07-11-2003, 01:29 AM	#37 (permalink)
TIO Addict Location: The Land Down Under	Debaser has it right. Sure, you can name any number, and show me that that number is no longer in the bag, but I can always name a number that is still in the bag. __________________ Strewth

07-11-2003, 05:16 AM	#38 (permalink)
duckznutz Addict Location: Brook Cottage, Lanark, Scotland	Thanks bermuDa . . no-one is immune to flattery! Did I mention that I think you are a wonderful person! __________________ Where your talents and the needs of the world cross . . there lies your vocation.