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Index > Heap > What is the best pie you can get with 9 digits?

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bitRAKE



Joined: 21 Jul 2003
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bitRAKE

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Post 07 Mar 2008, 23:26
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edfed



Joined: 20 Feb 2006
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edfed
consider this chain:

0: 1
1: 11
2: 21
3: 1211
4: 111221
5: 312211
6: 13112221
7: 1113213211
8: 31131211131221

what is the next number?
is it possible to have a 4 in the a number of this chain?
what is the value of 1000: ?
Post 07 Mar 2008, 23:39
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bitRAKE



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bitRAKE
I know that series - should be on a google search, too. Would you like a generative program - should be easy in x86 - wonder how small I can make it?

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Post 08 Mar 2008, 00:26
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edfed



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edfed
me too.
i wonder the time i'll spend to make it more than it's size.
graphics? text? win32?
Post 08 Mar 2008, 00:30
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bitRAKE



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bitRAKE
Can't even be 3 3's - certainly not 4. I tried to upload 1000: but the board wouldn't let me.

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Post 08 Mar 2008, 01:14
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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revolution
edfed: That chain has nothing to do with this puzzle.
Post 08 Mar 2008, 01:21
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revolution
When all else fails, read the source


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revolution
r22 wrote:
|[0,INF)|

There we go, the number of elements in the range 0 <= x < INF. A set less than INF can't have a count of INF, so I win.
And INF = ??? What is the number one less than INF ??? Not accept, no well defined.
Post 08 Mar 2008, 01:22
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victor



Joined: 31 Dec 2005
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victor
Let k be the current top entry under the "Purely Mathematical" section of revolution's list.

k is an infinite cardinal.

By König's theorem, the gimel function ] has the property ](k) > k for all infinite cardinals k.

So, here is my winning shot: ](k) . Twisted Evil

Refer to: http://en.wikipedia.org/wiki/Gimel_function .
Post 08 Mar 2008, 01:55
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revolution
When all else fails, read the source


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revolution
victor wrote:
Let k be the current top entry under the "Purely Mathematical" section of revolution's list.

k is an infinite cardinal.

By König's theorem, the gimel function ] has the property ](k) > k for all infinite cardinals k.

So, here is my winning shot: ](k) . Twisted Evil

Refer to: http://en.wikipedia.org/wiki/Gimel_function .
Okay, so that means your entry is ](Beth EEEw). But that is too long, 12 characters.

BTW, the current list:
Code:
Finites:
5.  9$$$$$$$$       bitRAKE
4.   9($^9$$$)       Tomasz Grysztar
3.   G($^G$$$)       Tomasz Grysztar (belatedly accepted)
2.      BB(BB(9))       Tomasz Grysztar
1.   (BB^9)(9)       Tomasz Grysztar (belatedly accepted)

Transfinites:
5.     Aleph-Z$$       MHajduk
4.   Beth-Z$$$       bitRAKE
3.   beth_w^w        Tomasz Grysztar
2.   Beth_EEE0       MHajduk
1.   Beth EEEw       revolution (shamelessly ripped from MHajduk's Beth_EEE0)    
Post 08 Mar 2008, 02:14
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bitRAKE



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bitRAKE
](Tav)

God only knows, lol. Laughing

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Post 08 Mar 2008, 02:47
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revolution
When all else fails, read the source


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revolution
](Dolly Parton) Now that is really big.
Post 08 Mar 2008, 02:50
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revolution
When all else fails, read the source


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revolution
bitRAKE wrote:
](Tav)
I found this here, it seems to be a collection of sets and is described as absolutely infinite. So I guess that means it is not a number. Not accept
Post 08 Mar 2008, 03:00
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sinsi



Joined: 10 Aug 2007
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sinsi
*

(because a wildcard matches everything)
Post 08 Mar 2008, 03:35
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revolution
When all else fails, read the source


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revolution
sinsi wrote:
*

(because a wildcard matches everything)
My white shirt matches everything but I'm not going to suggest it as an answer.
Post 08 Mar 2008, 03:43
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victor



Joined: 31 Dec 2005
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victor
Under the "Finites" section:

Since revolution accepts base-36, (BB^Z)(Z) is obviously much bigger than (BB^9)(9). Very Happy

Under the "Transfinites" section:

Since revolution does not accept my "always-win" entry, I would argue the following.

The written forms, "Beth xxxx", are, indeed, pronunciation of the Beth numbers. So, under the 9-character limit, the largest, yet "decent", entry is "Beth ten". Entries like "Beth EEEw" should be decarded! (Besides, I would question whether or not the construct "EEEw" is generally accepted!) Evil or Very Mad
Post 08 Mar 2008, 05:20
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revolution
When all else fails, read the source


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revolution
victor wrote:
(BB^Z)(Z)
Accept, a new number 1.
victor wrote:
Beth ten
Accept, but too small to make the top 5.
victor wrote:
I would question whether or not the construct "EEEw" is generally accepted!
Well it is revolutionarily accepted Razz

Can anyone do any better?
Post 08 Mar 2008, 06:10
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tom tobias



Joined: 09 Sep 2003
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tom tobias
victor wrote:
...the gimel function ] has the property ](k) > k for all infinite cardinals k. ...

(1) Has Dean's criticism of Goedel's incompleteness theorem been accepted by the broader mathematics community?
http://www.philosophyforum.com/forum/logic/930-biggest-mathematics-fraud-history.html
(2) To what extent, if any, does this "gimel" function depend upon Goedel's earlier (1947) articulation of the same idea?
http://books.google.com/books?id=lgDGTYNcOY4C&pg=PA172&lpg=PA172&dq=gimel+godel&source=web&ots=SC8xQKO0He&sig=d2gioeuMgt2-k6UroK7a3enp2wQ&hl=en
(3) Is there any relationship between Goedel's theorem (1931) and the "gimel" function of Bukovsky and Hechler?
http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorem
http://www.logique.jussieu.fr/~boban/pdf/Pcf.pdf
Post 08 Mar 2008, 09:59
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Tomasz Grysztar
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Joined: 16 Jun 2003
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Tomasz Grysztar
tom tobias wrote:
(1) Has Dean's criticism of Goedel's incompleteness theorem been accepted by the broader mathematics community?

It would be an interesting readin for me if it was a criticism on the mathematical grounds, however this whole thing is more similar to some kind of religious crusade than to a real justified mathematical reasoning.

And even philosophically speaking, some of his statements are way too confident. For example:
Quote:
If the logic he uses is not consistent then he cannot make a proof that is consistent.

Why is it "he cannot"? He may be just using a part of his logic that is unflawed to make some proof, and thus this proof would be completely consistent.
Post 08 Mar 2008, 11:15
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Borsuc



Joined: 29 Dec 2005
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Borsuc
Z^(1/dx)! Razz
Post 08 Mar 2008, 12:42
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MHajduk



Joined: 30 Mar 2006
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MHajduk
victor wrote:
Entries like "Beth EEEw" should be decarded! (Besides, I would question whether or not the construct "EEEw" is generally accepted!) Evil or Very Mad
Image
Post 08 Mar 2008, 12:43
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