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

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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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Re: small numbers

DOS386 wrote:
ro90("8")

What is that?

Oh, do you mean rotate "8" 90 degrees?
Post 06 Mar 2008, 06:33
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Tomasz Grysztar
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Joined: 16 Jun 2003
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revolution wrote:
But it doesn't matter really, because, so far, no one has come even close to putting a REALLY big number.


OK, going further. Wink

BB(BB(9))

(BB^9)(9)

I use BB to denote the busy beaver function, though there are various notations - here we really may get a notation problem.
Post 06 Mar 2008, 06:41
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DOS386



Joined: 08 Dec 2006
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> Oh, do you mean rotate "8" 90 degrees?

YES.
Post 06 Mar 2008, 06:47
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bitRAKE



Joined: 21 Jul 2003
Posts: 2624
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revolution wrote:
But it doesn't matter really, because, so far, no one has come even close to putting a REALLY big number.

When I first replied there was the thought that you had already composed a number of significant size, and this comment follows in that direction - as if thus far we have missed an operation.

_________________
The generation of random numbers is too important to be left to chance - Robert R Coveyou


Last edited by bitRAKE on 06 Mar 2008, 07:01; edited 1 time in total
Post 06 Mar 2008, 07:00
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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Tomasz Grysztar wrote:
BB(BB(9))

Accept, now we are getting close.


Tomasz Grysztar wrote:
(BB^9)(9)

Hmm, I need to think about that one. BB^9 is what - maybe BB(BB(BB(BB(BB(BB(BB(BB(BB(9)))))))))???
Post 06 Mar 2008, 07:00
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Tomasz Grysztar
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Joined: 16 Jun 2003
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revolution wrote:

Tomasz Grysztar wrote:
(BB^9)(9)

Hmm, I need to think about that one. BB^9 is what - maybe BB(BB(BB(BB(BB(BB(BB(BB(BB(9)))))))))???


Yes, (BB^9)(9)=BB(BB(BB(BB(BB(BB(BB(BB(BB(9))))))))).
Post 06 Mar 2008, 07:11
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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Tomasz Grysztar wrote:

revolution wrote:

Tomasz Grysztar wrote:
(BB^9)(9)

Hmm, I need to think about that one. BB^9 is what - maybe BB(BB(BB(BB(BB(BB(BB(BB(BB(9)))))))))???


Yes, (BB^9)(9)=BB(BB(BB(BB(BB(BB(BB(BB(BB(9))))))))).

I can't find any supporting evidence, all I have seen use a subscript notation for the iterated BB function. Kind of like this:

BB9(9)

But of course it can't be done in normal ASCII so like I have written would not be accepted.
Post 06 Mar 2008, 07:16
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MHajduk



Joined: 30 Mar 2006
Posts: 5914
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Re: What is the largest number you can write in 9 characters

revolution wrote:
You are allowed a maximum of nine ASCII characters (0x20-0x7e) only, this includes spaces and brackets etc., to write a representation of a number.

All standard mathematical symbols and functions etc. are allowed.

So I will start the ball rolling with:

"9+9+9+9+9"

But I'm sure you can do better.

Nobody said that we have to think only about integer or real numbers. I want to use here cardinal number. Every number given before we can treat as a size of finite set of elements (if given number x is real we can obtain natural taking E(|x|), where |x| is absolute value of x, E(z) - entier from z, in other words [z] or int(z)), i.e. finite cardinal number.

Here is my proposition:
Image

Code:
Aleph-0

i.e. size of set of natural numbers, which is greater from any finite cardinal number.

Aleph-0
Aleph number
Post 06 Mar 2008, 08:48
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Tomasz Grysztar
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Aleph-9$$
Very Happy

However it could be a little more interesting it you chose to go into ordinal numbers instead of cardinal numbers. Wink


Last edited by Tomasz Grysztar on 06 Mar 2008, 08:55; edited 2 times in total
Post 06 Mar 2008, 08:53
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MHajduk



Joined: 30 Mar 2006
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I supposed that you write something like that... Laughing
Post 06 Mar 2008, 08:55
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revolution
When all else fails, read the source


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Re: What is the largest number you can write in 9 characters

MHajduk wrote:
Aleph-0

Accept, getting warmer.
Post 06 Mar 2008, 09:04
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revolution
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Joined: 24 Aug 2004
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Tomasz Grysztar wrote:
Aleph-9$$

Accept.

Can anybody do better?
Post 06 Mar 2008, 09:07
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edfed



Joined: 20 Feb 2006
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oo^oo^1/0
Post 06 Mar 2008, 09:28
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revolution
When all else fails, read the source


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edfed wrote:
oo^oo^1/0

Reject, I think you know why.
Post 06 Mar 2008, 09:48
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MHajduk



Joined: 30 Mar 2006
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Location: Poland

revolution wrote:

Tomasz Grysztar wrote:
Aleph-9$$

Accept.

Can anybody do better?

Hehe, of course we can... Very Happy Because we can use non-decimal numeral systems then we can use our beloved Wink hexadecimal system and write

Code:
Aleph-F$$

which is greater than Aleph-9$$ (9 < F=15).

Some programmers even go far and extend this notation to numeral system with base 36 (digits 0, 1, ..., 9 and all English letters A, B, ..., Z). Then in such system we can write

Code:
Aleph-Z$$

Very Happy
Post 06 Mar 2008, 09:49
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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Location: 1I/ʻOumuamua

MHajduk wrote:
... we can use non-decimal numeral systems then we can use our beloved Wink hexadecimal system and write

Code:
Aleph-F$$

which is greater than Aleph-9$$ (9 < F=15).

I hadn't thought of that, but looks like fun so I accept.

MHajduk wrote:
Some programmers even go far and extend this notation to numeral system with base 36 (digits 0, 1, ..., 9 and all English letters A, B, ..., Z). Then in such system we can write

Code:
Aleph-Z$$

Very Happy

Okay, why not, I accept base 36.

Can anyone do any better? We're still not there yet.
Post 06 Mar 2008, 10:10
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Tomasz Grysztar
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The next step is aleph_w Smile

It really should be written like this:
Image
but I've found the "aleph_w" writing quite usual in emails etc.
Post 06 Mar 2008, 10:12
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Tomasz Grysztar
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And kudos to anyone who is able to describe some totally indescribable cardinal in the 9 characters. Wink Very Happy
Post 06 Mar 2008, 10:14
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MHajduk



Joined: 30 Mar 2006
Posts: 5914
Location: Poland

Tomasz Grysztar wrote:
The next step is aleph_w Smile

It really should be written like this:
Image
but I've found the "aleph_w" writing quite usual in emails etc.

You mean "aleph-omega" of course. Smile
Post 06 Mar 2008, 10:29
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Tomasz Grysztar
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The other name, right. :>
Post 06 Mar 2008, 10:40
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