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Author
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
DOS386 wrote:
ro90("8")
What is that?

Oh, do you mean rotate "8" 90 degrees?
06 Mar 2008, 06:33
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
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.

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.
06 Mar 2008, 06:41
DOS386

Joined: 08 Dec 2006
Posts: 1903
DOS386
> Oh, do you mean rotate "8" 90 degrees?

YES.
06 Mar 2008, 06:47
bitRAKE

Joined: 21 Jul 2003
Posts: 2808
Location: dank orb
bitRAKE
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.

_________________

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

Joined: 24 Aug 2004
Posts: 16951
revolution
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)))))))))???
06 Mar 2008, 07:00
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
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))))))))).
06 Mar 2008, 07:11
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
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.
06 Mar 2008, 07:16
MHajduk

Joined: 30 Mar 2006
Posts: 6032
Location: Poland
MHajduk
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:

Code:
`Aleph-0    `
i.e. size of set of natural numbers, which is greater from any finite cardinal number.

Aleph-0
Aleph number
06 Mar 2008, 08:48
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
Aleph-9\$\$

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

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

Joined: 30 Mar 2006
Posts: 6032
Location: Poland
MHajduk
I supposed that you write something like that...
06 Mar 2008, 08:55
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
MHajduk wrote:
Aleph-0
Accept, getting warmer.
06 Mar 2008, 09:04
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
Tomasz Grysztar wrote:
Aleph-9\$\$
Accept.

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

Joined: 20 Feb 2006
Posts: 4225
Location: 2018
edfed
oo^oo^1/0
06 Mar 2008, 09:28
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
edfed wrote:
oo^oo^1/0
Reject, I think you know why.
06 Mar 2008, 09:48
MHajduk

Joined: 30 Mar 2006
Posts: 6032
Location: Poland
MHajduk
revolution wrote:
Tomasz Grysztar wrote:
Aleph-9\$\$
Accept.

Can anybody do better?
Hehe, of course we can... Because we can use non-decimal numeral systems then we can use our beloved 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\$\$    `
06 Mar 2008, 09:49
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 16951
revolution
MHajduk wrote:
... we can use non-decimal numeral systems then we can use our beloved 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\$\$    `
Okay, why not, I accept base 36.

Can anyone do any better? We're still not there yet.
06 Mar 2008, 10:10
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
The next step is aleph_w

It really should be written like this:

but I've found the "aleph_w" writing quite usual in emails etc.
06 Mar 2008, 10:12
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
And kudos to anyone who is able to describe some totally indescribable cardinal in the 9 characters.
06 Mar 2008, 10:14
MHajduk

Joined: 30 Mar 2006
Posts: 6032
Location: Poland
MHajduk
Tomasz Grysztar wrote:
The next step is aleph_w

It really should be written like this:

but I've found the "aleph_w" writing quite usual in emails etc.
You mean "aleph-omega" of course.
06 Mar 2008, 10:29
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7543
Location: Kraków, Poland
Tomasz Grysztar
The other name, right. :>
06 Mar 2008, 10:40
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