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Author
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7725
Location: Kraków, Poland
Tomasz Grysztar
revolution wrote:
Okay, you're describing a bit-reflected version of standard integer binary. But even a non-bit-reflected version still has -1 as the "greatest" element.

It's not bit-reflected, because you cannot 'reflect' it - it has the beginning, but doesn't have the end, so you cannot start 'from the other side', as there is no 'other side'. That's why p-adic numbers have no natural order.

revolution wrote:

Can you point out if I have made a mistake in this puzzle?

Specifically have I made a comparison error in the two lists? Maybe comparing things that can't be compared? Or allowing something that makes no sense?

That's a bit tricky. You see, you can compare ordinal with cardinal, by comparing the cardinality of that ordinal with actual cardinal. However this leads to some inconsistencies.
For example omega and omega^2, and even epsilon_0 all have the cardinality of aleph_0. So you have something like:

aleph_0 "=" omega < omega^2 < epsilon_0 "=" aleph_0
07 Mar 2008, 10:50
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
It would be a shame to have to disallow all the Aleph and Beth type answers, they were quite fun.

But if it means better consistency then perhaps it is best to eliminate that part and shift focus to the more "normal" numbers with the "(BB^9)(9)" thing currently leading.
07 Mar 2008, 10:59
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7725
Location: Kraków, Poland
Tomasz Grysztar
revolution wrote:
But if it means better consistency then perhaps it is best to eliminate that part and shift focus to the more "normal" numbers with the "(BB^9)(9)" thing currently leading.

Aleph and beth are quite OK themselves, if only we choose to concentrate on cardinals only.
07 Mar 2008, 11:25
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
Okay folks, cardinals are in, bishops are out, oops, I mean ordinals are out.

There is still a lot of room for improvement in the current numbers!
07 Mar 2008, 11:41
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7725
Location: Kraków, Poland
Tomasz Grysztar
revolution wrote:
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.
Okay, I accept email translations of this sort of thing. But only because it won't help you at all.

OK, so let's go for beth_w^w now.
07 Mar 2008, 12:06
r22

Joined: 27 Dec 2004
Posts: 805
r22
beth_w^w\$

blatantly ripped off from the post above.
07 Mar 2008, 12:54
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7725
Location: Kraków, Poland
Tomasz Grysztar
r22 wrote:
beth_w^w\$

blatantly ripped off from the post above.

You'd need to define the \$ operator for transfinite ordinals first.
07 Mar 2008, 13:11
r22

Joined: 27 Dec 2004
Posts: 805
r22
SUMn<INFz - illegible

n,0<n<INF - this would be a set not a number

|n|,n!=INF - count of the set of all numbers not infinitiy DOH! 10 chars

I've got nothin'
07 Mar 2008, 13:18
r22

Joined: 27 Dec 2004
Posts: 805
r22
re: Tomasz

beth_w^9w ?
07 Mar 2008, 13:20
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
Tomasz Grysztar wrote:
revolution wrote:
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.
Okay, I accept email translations of this sort of thing. But only because it won't help you at all.

OK, so let's go for beth_w^w now.
Hey, no fair, you used an ordinal. :sulk:
07 Mar 2008, 13:44
asmhack

Joined: 01 Feb 2008
Posts: 431
asmhack
or you are pro at maths.. or i am too dumb or outdated..

CRAP-X\$\$\$
07 Mar 2008, 13:47
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
asmhack wrote:
CRAP-X\$\$\$
Accept if you can give the value.
07 Mar 2008, 13:58
Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7725
Location: Kraków, Poland
Tomasz Grysztar
revolution wrote:
Tomasz Grysztar wrote:
OK, so let's go for beth_w^w now.
Hey, no fair, you used an ordinal. :sulk:

w^w is an ordinal, but beth_w^w is a cardinal. Aleph and beth take ordinals as indexes, but themselves they are cardinals.
07 Mar 2008, 14:15
asmhack

Joined: 01 Feb 2008
Posts: 431
asmhack
pfff
ok...
it's the biggest number in the galaxy.. it can't feet in 3D dimension even..
ps: don't search for that in wiki.. it's undocumented
07 Mar 2008, 14:18
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
Tomasz Grysztar wrote:
w^w is an ordinal, but beth_w^w is a cardinal. Aleph and beth take ordinals as indexes, but themselves they are cardinals.
Alright, I accept.

That totally blows away the answer I had, now I will have to rethink and see if I can beat ya .

So we have a new number 1.
Code:
```Purely mathematical:
5.      Aleph-9\$\$       Tomasz Grysztar
4.   Aleph-F\$\$       MHajduk
3.   Aleph-Z\$\$       MHajduk
2.   Beth-Z\$\$\$       bitRAKE
1.   beth_w^w        Tomasz Grysztar    ```

Can anyone do any better?
07 Mar 2008, 14:21
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
asmhack wrote:
it's undocumented
undocumented = unacceptable. If you can provide independent supporting documents and it's value then I accept.
07 Mar 2008, 14:24
asmhack

Joined: 01 Feb 2008
Posts: 431
asmhack
and what is the value of ALEPH ??? aleph + 1 = ???
see ? it's not a number... it is a SET of numbers
07 Mar 2008, 14:25
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
Location: In your JS exploiting you and your system
revolution
I looked up your proposed submission and found this, does it have a value? Seems quite valueless to me.
07 Mar 2008, 14:27
asmhack

Joined: 01 Feb 2008
Posts: 431
asmhack
|-R-R|
07 Mar 2008, 14:50
bitRAKE

Joined: 21 Jul 2003
Posts: 2915
Location: [RSP+8*5]
bitRAKE
There appears to be a character not used in any solution, and a concept not used in any submission thus far. I'm really at a loss as to what you have in mind. Nor can I really connect with the magnitude of the numbers currently represented. Not that any of that has swayed my curiosity in the slightest.

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