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thebruce
Dances With Wikis

Joined: 16 Aug 2004
Posts: 6865
Location: Kitchener, Ontario

 tanner wrote: well if: x = 99.999999... (approaching 100) 10x = 999.999999... 10x - x = 900.000000... 10x - x = 900 x = 100 x has reached number 100

the difference is 100... obviously x can't be 99.9rpt AND 100 simultaneously... but I don't have the mathematical proof to lay it out
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Posted: Tue Dec 21, 2004 12:32 pm
Shish
Boot

Joined: 24 Nov 2004
Posts: 51

> x approaches 100% but never reaches it

it remains 1/inf away from 100%, and as the above shows, 1/inf = 0

> 10x = 999.999999...
> 10x - x = 900.000000...

given that x = 100, then 10x-x = 899.999; and lo, if the theory is wrong then it's just wrong, and if it's right then it /proves/ itself wrong.

As said, I'm quite sure this sort of math belongs in the same place as infinite competing forces, perpetual motion machines, proving a negative, and that sort of stuff...
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Posted: Tue Dec 21, 2004 1:08 pm
jesterkik
Boot

Joined: 02 Dec 2004
Posts: 10
Location: Illinois

 Shish wrote: > 10x = 999.999999... > 10x - x = 900.000000...

The problem is the 10x -x line. Mathematically, you can't subtract 0.99~ to get zeros because it is infinitly repeating. At least, says my calc professor.
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Posted: Tue Dec 21, 2004 1:15 pm
tanner
Entrenched

Joined: 21 May 2003
Posts: 875
Location: (x,y,z,t,i, ...)+

your calc is limited --- each 9 subtracts from the nine in the larger number --- there are no carries therefore it works till infinity -- if you subract 99 from 99.999999... you get 0.9999999... --- i guarantee my proof is correct and i invite you to ask any great mathematical genius in the universe to check it

.

.
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"And the princess and the prince discuss what's real and what is not,
But it doesn't matter inside the Gates of Eden" - BD

Posted: Tue Dec 21, 2004 1:53 pm
Seej
Unfettered

Joined: 30 Nov 2004
Posts: 614

Seej wrote:
 Rei wrote: Calling them E numbers just makes me think of the codes that you get for food. however i dont think that they have anything to do with these... im just thinking out loud.

Yeah, E numbers in food....

......blah, blah, blah.........

......It's what's known to mathematicians as an irrational number, which basically means the numbers keep on going after the decimal point for ever........

........blah, blah, blah.

Aaaaand that is officially the last time I'm ever gonna mention irrational numbers around you lot. Please, let it go

Posted: Tue Dec 21, 2004 1:58 pm
SilentAvenger
Boot

Joined: 23 Oct 2004
Posts: 44

Actually, its a mathematical proven fact that 0.999999 (rep) is equal to 1. Its not lim x->1, its 1. lim x->1 is the biggest (or smallest) possible number which is smaller than 1 (1 - 1/(infinity), cause lim 1/(infinity) -> 0(+)).

Anyways, thebruce, an infinite chance of something happening means that it will happen an infinite number of times. Say, there is an infinite chance of 1 appearing in the string 0.123451234512345 (rep) means that 1 will appear an infinite number of times.

Posted: Tue Dec 21, 2004 2:07 pm
tanner
Entrenched

Joined: 21 May 2003
Posts: 875
Location: (x,y,z,t,i, ...)+

thanks avenger -- i thought i was on my own in here
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"And the princess and the prince discuss what's real and what is not,
But it doesn't matter inside the Gates of Eden" - BD

Posted: Tue Dec 21, 2004 2:14 pm
neon snake
Veteran

Joined: 18 Mar 2004
Posts: 70
Location: Chelmsford, UK

*shouts*

Please, PMs, give us more postcards or clues! Or something, anything!

*sobs* Look at what you've done to us...we're rehashing lectures from ten years ago (in my case) on the theory of infinite numbers...*sobs*

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'To know, yet to think that one does not know is best. Not to know, yet to think that one knows will lead to difficulty.'
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Posted: Tue Dec 21, 2004 2:16 pm
Olorin
Unfettered

Joined: 04 Nov 2004
Posts: 612
Location: Gainesville, FL

 neon snake wrote: *shouts* Please, PMs, give us more postcards or clues! Or something, anything! *sobs* Look at what you've done to us...we're rehashing lectures from ten years ago (in my case) on the theory of infinite numbers...*sobs*

Yeah, and in a minute or two someone will mention L'Hospital's rule and then...
...oh....

...oopsie ?

F.O.R.

Posted: Tue Dec 21, 2004 2:36 pm
thebruce
Dances With Wikis

Joined: 16 Aug 2004
Posts: 6865
Location: Kitchener, Ontario

EDIT: haha! yeah, we need the arg to start... but this is fun for now I'm learning stuff

 SilentAvenger wrote: Anyways, thebruce, an infinite chance of something happening means that it will happen an infinite number of times. Say, there is an infinite chance of 1 appearing in the string 0.123451234512345 (rep) means that 1 will appear an infinite number of times.

yes but by definition you've already stated that a parameter of that repeating number is that it includes 1. You know that 12345 is repeated. Therefore you have a maximum from which to calculate a chance. 1 in 5, times infinity, therefore an infinite # of times...

if you have an infinite non-repeating number, and say you quote the first 5 numbers - 1.92395etc - then you can easily say the chances of 2, or 5 appearing are 100%, just as you can say the chances of 23 or 395 appearing are 100%... but you can't prove that 8 will appear until you reach it, and you can't prove that 12936419325 will appear until you reach it. If you have no maximum, any sequence of code could at appear at any point of that infinite length number. So in theory, there's a chance you may never reach any particular sequence, because you can state that from the 100,000th to the 101,000th number is a unique 1000 number length sequence... so you can say the 1Mth to the 2Mth number is a unique 1M length sequence... there are an infinite number of sequences to be found in the infinite length #. So who's to say that the sequence you choose may or may not be found, or where?

Here's an example... if you state that the bounds of a random number must include at least one of each of the numbers 0-9, then the chance of a any single number appearing is 100%.

If you simply state that it's a truly random infinite length number, with no definition of its contents, then the chance of any single number or any sequence of numbers appearing merely approaches 100%, because you will never know if it exists in the number until you reach it. The chances of a smaller sequence of numbers appearing in e is far greater than a much longer sequence of numbers, sure, but will it ever be 100%? Essentially, no. For all intents and purposes, yes. But no matter how far you go into infinity, there will always be a random number to that point that will not have given you the sequence you were looking for, however small that possibility may be (approaching 0%)
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Posted: Tue Dec 21, 2004 3:05 pm
neon snake
Veteran

Joined: 18 Mar 2004
Posts: 70
Location: Chelmsford, UK

Nearly, but not quite. Your argument hinges on stopping at a point (if you count up the nth digit in the infinitely long string that is 'e', there is a bigger chance that you will have found a small string than a large string).

However, 'e' is (to the best of all our knowledge) infinitely long, non-repeating, has no discernable pattern and contains all digits (0-9) - therefore, all possible strings are contained in it.

To try and demonstrate -

Is the digit '8' contained in 'e'? Yes, its the 3rd digit after the decimal point.

Is the string '452' contained in 'e'? Yes, 14 after the decimal point.

Is the string '69811250996' contained in 'e'? Yes, around the 700 mark, just eyeballing it.

I've picked strings that I can see in the first 1000, but you get the point. The longer the string, the further you have to look, but it WILL always be there, you just have to keep looking.

The chance of a 200 digit string being in 'e' is the same as the chance of the string '452' being in 'e' - ie. '1', 100%. It is in there, somewhere.
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'To know, yet to think that one does not know is best. Not to know, yet to think that one knows will lead to difficulty.'
Lao Tzu

Posted: Tue Dec 21, 2004 3:25 pm
Rei
Boot

Joined: 14 Dec 2004
Posts: 43
Location: spoo-kehhh

For all of you strugalling to understand the concept of infinity (or my spelling) I advise you read the introduction to Hitch Hikers Guide to the Galaxy.
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Applying my non linear logic to everything!

Posted: Tue Dec 21, 2004 3:48 pm
rose
...and then Magic happens

Joined: 26 Nov 2003
Posts: 4104

reverse psychology

neon snake wrote:

 Quote: *shouts* Please, PMs, give us more postcards or clues! Or something, anything! *sobs* Look at what you've done to us...we're rehashing lectures from ten years ago (in my case) on the theory of infinite numbers...*sobs*

I have a bit of well meant, but probably unwelcomed advice for you: learning to deal with the pace of this game may be essential to your maintaining your mental health when the game actually starts.

Or, perhaps a more convincing - though twisted - thought: you might want to consider that the PMs actually enjoy tantalizing us. So the more we beg for stuff, the more we are playing into their evil plans and the less likely they are to give it to us. Perhaps an attitude of profound indifference, which I sincerely doubt we could successfully pull off, would be the way to lure some new information from them.

Posted: Tue Dec 21, 2004 3:52 pm
thebruce
Dances With Wikis

Joined: 16 Aug 2004
Posts: 6865
Location: Kitchener, Ontario

 neon snake wrote: Nearly, but not quite. Your argument hinges on stopping at a point (if you count up the nth digit in the infinitely long string that is 'e', there is a bigger chance that you will have found a small string than a large string).

thought I said that

 Quote: However, 'e' is (to the best of all our knowledge) infinitely long, non-repeating, has no discernable pattern and contains all digits (0-9) - therefore, all possible strings are contained in it.

My point is you can never know that... it's an interpretation of the evidence. The only evidence we have is that string X is contained in e where we know and have found each value of X. Logically you can't conclude that ALL possible permutations of any length of sequence in X is contained in e, because we don't know all possible values of X.

However, the interpretation of the evidence - based on a staggering number of known values of X, they have all been found to the degree e has been calculated - shows that we can assume any value of X can be found in e at some point. This means we can't say as fact that all values of X can be found in e, be we can assume they can be.

 Quote: Is the digit '8' contained in 'e'? Yes, its the 3rd digit after the decimal point.

Because we've found it.

 Quote: Is the string '452' contained in 'e'? Yes, 14 after the decimal point.

Because we've found it.

 Quote: Is the string '69811250996' contained in 'e'? Yes, around the 700 mark, just eyeballing it.

Because we've found it.

 Quote: I've picked strings that I can see in the first 1000, but you get the point. The longer the string, the further you have to look, but it WILL always be there, you just have to keep looking.

Precisely.

 Quote: The chance of a 200 digit string being in 'e' is the same as the chance of the string '452' being in 'e' - ie. '1', 100%. It is in there, somewhere.

in the case of e, we can give as many digits or sequences that we know exist in e up to the degree that e has been calculated. Beyond that, if we don't know the next digit, we don't know what the next possible sequence may be...

anyway, what I'm saying is, that given any random number, with no predefined guidelines as to its contents, there is a chance that, for instance, the random number might end up being 1.11111111111111etc. It's a random number whice has a chance of existing as next to 0, but there is that chance that every random digit in the number will be 1. If the chance is 10% per digit, infinity times, the chance of a random number consisting of solely 1's approaches impossible, but will never reach impossible because it's still a theoretical possibility... in the same way, the chances of every number 0-9 appearing in the infinite # is slightly less than the chance that all but one number will appear in the infinite #... So the chance of any number or any sequence of numbers appearing in a random infinite number is anywhere from approaching impossible to approaching definite.

My head is spinning... my head a-splode philosophy...? :S
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Posted: Tue Dec 21, 2004 4:35 pm
neon snake
Veteran

Joined: 18 Mar 2004
Posts: 70
Location: Chelmsford, UK

I know you said it. That's why it's your argument.
I know we've found them. The demonstration would fall pretty flat if I picked numbers we hadn't.
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'To know, yet to think that one does not know is best. Not to know, yet to think that one knows will lead to difficulty.'
Lao Tzu

Posted: Tue Dec 21, 2004 4:53 pm
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