Number that cannot be written

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Number that cannot be written
« on: January 31, 2008, 04:01:27 PM »
I dont know if im gonna do this one justice or not, but its an interesting paradox. Im saying its philosophy because it sure aint any of the others.

Ok, so. You take every number between 0 and 1 (an infinite ammount)
You the lengthen them to an infinite length by adding 0s on the end
so 0.1 becomes 0.1000000000000000(etc)
then, you take the first digit of the first number, and the second digit of the second number, and the nth digit of the nth number and so on. and you call that number X
then you take number X, and write it out again, but you add 1 to all of the digits (9 looping round to 0). call this number Y
This number has to be different to all the other numbers in the list, as X contained one digit from every digit in the list and number Y has every digit different to the one in number X.

Hense, we have not written number Y in the list, even though it contains every number between 0 and 1.
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Trekky0623

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Re: Number that cannot be written
« Reply #1 on: January 31, 2008, 04:12:10 PM »
Huh?

Re: Number that cannot be written
« Reply #2 on: January 31, 2008, 04:25:30 PM »
Its a lot easier to describe it to someone in person.

id draw a diagram, but it looks a little odd when you have to write "goes on for infinity" on every side

What isnt making sense? ill do my best to explain it in greater detail.
ny Conspiricy without a secret society more than 1000 years old isn't worth thinking about

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Raist

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Re: Number that cannot be written
« Reply #3 on: January 31, 2008, 04:32:25 PM »
You can't write any number that goes into infinity.

But I believe you are talking about a number that has 2 degrees of infinity. Those are a pain.

Re: Number that cannot be written
« Reply #4 on: January 31, 2008, 04:33:06 PM »
Perhaps this is over my head, as I'm certainly no mathematician, but there are only two logical possibilities:

1. It is not a number between 0 and 1. Furthermore, since nothing in that list leads me to believe it is negative, you have written a number greater than 1.
2. It actually is a number between 0 and 1.

Now, let's shorten X to make it reasonable to work with (though we actually can't write X as it would continue on forever and the smallest number above 0 would be an infinite amount of zeros with a 1 tacked on the end). For our purposes 4 digits past the decimal will certainly do. So, we can call X 0.0159. To get Y we add 1 to each digit. Quickly we find which of the two possible numbers has been written. adding one to each digit gives us 1.1270. Hopefully that basic addition is easy enough to figure out, it goes like this:

_0.0159 (The underscore is to help line up the numbers)
+1.1111
=
_1.1270

So we've actually written a number greater than 1. If you don't add 1 to the one's digit place (the zero to the left of the decimal point) then you aren't actually adding 1 to all the digits. If this were the case then we would have a number between 0 and 1 and would therefore have already written it. Furthermore, theoretically all these numbers would be infinite in nature, I just shortened them so it could be represented and seen easily.

So we haven't written Y and it probably does contain every number between 0 and 1, but this is because it is greater than 1 with an infinite number decimals afterwards.
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Bushido

Re: Number that cannot be written
« Reply #5 on: January 31, 2008, 04:42:36 PM »
יהוה

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Trekky0623

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Re: Number that cannot be written
« Reply #6 on: January 31, 2008, 05:07:09 PM »


LOL FIREFOX IMAGE BLOCK, BITCH!

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Raist

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Re: Number that cannot be written
« Reply #7 on: January 31, 2008, 05:11:22 PM »


LOL FIREFOX IMAGE BLOCK, BITCH!
Thanks for reminding me. Now images from there don't show up for me either.

pwned.

Re: Number that cannot be written
« Reply #8 on: January 31, 2008, 09:14:05 PM »

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Midnight

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Re: Number that cannot be written
« Reply #9 on: January 31, 2008, 10:14:30 PM »
This thread proves the existence of intelligent life...anywhere but here.
My problem with his ideas is that it is a ridiculous thing.

Genius. PURE, undiluted genius.

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Bushido

Re: Number that cannot be written
« Reply #10 on: February 01, 2008, 07:51:01 AM »
This thread proves the existence of intelligent life...anywhere but here.

And now you are in it.

Re: Number that cannot be written
« Reply #11 on: February 01, 2008, 10:41:01 AM »

_0.0159 (The underscore is to help line up the numbers)
+1.1111
=
_1.1270

So we've actually written a number greater than 1. If you don't add 1 to the one's digit place (the zero to the left of the decimal point) then you aren't actually adding 1 to all the digits. If this were the case then we would have a number between 0 and 1 and would therefore have already written it. Furthermore, theoretically all these numbers would be infinite in nature, I just shortened them so it could be represented and seen easily.


Im going with the second option. You don't add one to the first digit, sorry that was my fault entirely in te explanation. This should work for every integer between 0 and infinite as well, but i find its easier to work with 0 and 1 and include decimals. If you completely ignore the "0." part when doing all of the changes then it makes my explanation easier to understand, id guess.

And while we should have written it, we can't have as we have changed every digit. For example again using shortened digits.

it cant be the first digit in the list 0.0159 because Y starts 0.1260, but maybe 0.1260 occurs somewhere else?
Obviously it does. But by being in the list of numbers, 0.1260 has at least one digit of the same value in the same place as in number X and therefore has at least one digit different in number Y.
ny Conspiricy without a secret society more than 1000 years old isn't worth thinking about

Re: Number that cannot be written
« Reply #12 on: February 01, 2008, 03:38:39 PM »

Im going with the second option. You don't add one to the first digit, sorry that was my fault entirely in te explanation. This should work for every integer between 0 and infinite as well, but i find its easier to work with 0 and 1 and include decimals. If you completely ignore the "0." part when doing all of the changes then it makes my explanation easier to understand, id guess.

And while we should have written it, we can't have as we have changed every digit. For example again using shortened digits.

it cant be the first digit in the list 0.0159 because Y starts 0.1260, but maybe 0.1260 occurs somewhere else?
Obviously it does. But by being in the list of numbers, 0.1260 has at least one digit of the same value in the same place as in number X and therefore has at least one digit different in number Y.

Something still doesn't seem quite right. I don't think Y, 0.1260 in our example, has a different digit than the 'same' number from the list. We've only added 1 to every digit. We made 0.0 into 0.1 and if you carry that out into infinity it doesn't change the fact that that number is still between 0 and 1, and since we've written every number from 0 to 1, somewhere on our list of already written numbers. It may very well be different from X, but I contend that it is still on the list, as X is not every number on the list, but a combination of every number on the list.

Do you know any experts we could ask?
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Bushido

Re: Number that cannot be written
« Reply #13 on: February 01, 2008, 04:02:45 PM »
I dont know if im gonna do this one justice or not, but its an interesting paradox. Im saying its philosophy because it sure aint any of the others.

Ok, so. You take every number between 0 and 1 (an infinite ammount)
You the lengthen them to an infinite length by adding 0s on the end
so 0.1 becomes 0.1000000000000000(etc)
then, you take the first digit of the first number, and the second digit of the second number, and the nth digit of the nth number and so on. and you call that number X
then you take number X, and write it out again, but you add 1 to all of the digits (9 looping round to 0). call this number Y
This number has to be different to all the other numbers in the list, as X contained one digit from every digit in the list and number Y has every digit different to the one in number X.

Hense, we have not written number Y in the list, even though it contains every number between 0 and 1.

The set of all real numbers between 0 and 1 is uncountable. You fail.

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Germanicus

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Re: Number that cannot be written
« Reply #14 on: February 02, 2008, 03:44:36 PM »
The only number that can't be written that we have named is googelplex

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Raist

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Re: Number that cannot be written
« Reply #15 on: February 02, 2008, 03:48:13 PM »
The only number that can't be written that we have named is googelplex
It can be written. Just the size would hamper the writing process.

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Germanicus

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Re: Number that cannot be written
« Reply #16 on: February 02, 2008, 04:22:03 PM »

Quote
It can be written. Just the size would hamper the writing process.

Quoth Wikipedia;

Quote
Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.



Re: Number that cannot be written
« Reply #17 on: February 02, 2008, 04:51:51 PM »
Thats more of a technicality than an actual impossibility.

And Zanmor, i know it doesnt make any sense, if you look at it one way, it must be tehre cause they all are, but look at it another and it cant be there.

Perhaps the conclusion is that somethings just don't make any sense, even in maths and thinking about them too much hurts your head.
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Username

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Re: Number that cannot be written
« Reply #18 on: February 02, 2008, 04:55:15 PM »

Quote
It can be written. Just the size would hamper the writing process.

Quoth Wikipedia;

Quote
Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.



Just because it can't be written in decimal notation doesn't mean it can't be written...


Also its not the only number that can not be written in decimal notation.  Pi, or 2 googolplex, etc

Re: Number that cannot be written
« Reply #19 on: February 02, 2008, 09:16:03 PM »
Perhaps the conclusion is that somethings just don't make any sense, even in maths and thinking about them too much hurts your head.

lol, well that just reinforces my opinion after calc in high school ;)
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Loard Z

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Re: Number that cannot be written
« Reply #20 on: February 04, 2008, 01:22:50 AM »

Quote
It can be written. Just the size would hamper the writing process.

Quoth Wikipedia;

Quote
Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.



Quantum computers could store it.

if i remember, austria is an old, dis-used name for what is now Germany.
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Conspiracy Mastermind

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Re: Number that cannot be written
« Reply #21 on: February 04, 2008, 01:31:57 PM »

Quote
It can be written. Just the size would hamper the writing process.

Quoth Wikipedia;

Quote
Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.



Quantum computers could store it.

What if you wrote each zero to be 1 nanometre in height?
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Raist

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Re: Number that cannot be written
« Reply #22 on: February 05, 2008, 06:36:19 PM »
A show stated that writing it on paper in a standard font would fill up the entire universe +. This does not make the number unwritable. It simply makes it very inconvenient to write. You could write it in a computer with enough storage space and able to handle that large a number, you simply couldn't display it reasonably on the screen.

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Trekky0623

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Re: Number that cannot be written
« Reply #23 on: February 05, 2008, 06:41:34 PM »
A show stated that writing it on paper in a standard font would fill up the entire universe +. This does not make the number unwritable. It simply makes it very inconvenient to write. You could write it in a computer with enough storage space and able to handle that large a number, you simply couldn't display it reasonably on the screen.

Or you could show it in like Base ten billion.

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Raist

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Re: Number that cannot be written
« Reply #24 on: February 05, 2008, 06:50:31 PM »
or 10100100

which is a googleplex.

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Benocrates

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Re: Number that cannot be written
« Reply #25 on: February 05, 2008, 09:17:37 PM »
I think your all missing the point about the unwritable number of a googleplex. Your right in saying its not the only unwritable number, Pi and 2 googleplex are also unwritable but it's not a matter of display or inconvenience. There is a finite amount of information that exists in the universe. There is has been calculations done and I can't remember right now but there is an estimated amount of information in the universe and therefore even with all the matter in the universe being converted into computer storage or even quantum computing there will be a point at which no more numbers could be written or stored.
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Re: Number that cannot be written
« Reply #26 on: February 05, 2008, 09:21:19 PM »
I don't think there is such a point.  I think there is always a way to compress the information "enough".  Especially assuming our knowledge improves in compression and physics.

The example in this first post, as well as the example of pi shows us how good we are at 'storing' arbitrary amounts of data.
« Last Edit: February 05, 2008, 09:23:10 PM by Username »

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Benocrates

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Re: Number that cannot be written
« Reply #27 on: February 05, 2008, 09:24:28 PM »
This is a matter of intuition going against rational science. I'm not a physics expert so I can't articulate this very well but I did watch a lecture series called Beyond Belief that had an excellent lecture on this very topic. But there is a limit to information storage, no matter how effective technology becomes. There is a physical limit based on the estimated amount of matter/energy in the universe. If you accept the finite nature of the universe (most rational conclusion based on observation) you would have to accept this finite point, regardless of the current estimate.
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Re: Number that cannot be written
« Reply #28 on: February 05, 2008, 09:27:43 PM »
This is not a matter of intuition.

There are other ways to store information.   

You can store it, for example, as a function.  Or in relation to other data.  Or in relation to other functions

You have to mathematically show what you claim, and you haven't.

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Re: Number that cannot be written
« Reply #29 on: February 05, 2008, 09:29:59 PM »
It should be noted that this is hardly a religious or philosophical question.  Well, unless you consider math to be philosophy, which I suppose is valid in many ways.