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Author
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
bitRAKE wrote:
There appears to be a character not used in any solution,
Yes, so far 8/9 of my original idea, for trans-finites Tomasz has a better solution, but the finites section is still not near maximum.
bitRAKE wrote:
and a concept not used in any submission thus far.
2.5 of three concepts have been supplied.
bitRAKE wrote:
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.
07 Mar 2008, 15:02
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
revolution
If you accepted symbol "w" as a Latin graphic equivalent of Greek small omega (even not describing the same phoneme) I expect that you also accept Latin symbol "e" as a equivalent of Greek "epsilon" symbol (they describe the same phoneme).

My proposition is
Code:
`Beth_e_0    `
Because

e_0 = w^w^w^... > w^w

then

Beth_e_0 > Beth_w^w

Epsilon_nought (epsilon-0)
07 Mar 2008, 16:40
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
MHajduk wrote:
e_0
Sure, the rules are flexible, but I only accepted w because Tomasz said it was common in email. If you assure me that e_0 is also common in email (for Epsilon nought) then I will accept.
07 Mar 2008, 16:50
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
Okay:

E0
Wikipedia wrote:
E0 can refer to:

* ε0, in mathematics, the smallest transfinite ordinal number
(...)
Then we can even write shorter
Code:
`Beth_E0    `
07 Mar 2008, 16:56
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
So how about "Beth EZ\$\$"? Kinda weird with E and Z being different things, so maybe just "Beth E9\$\$"?
07 Mar 2008, 17:02
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
Oh I got it "Beth Ew^w".
07 Mar 2008, 17:04
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
Code:
`Beth_EEE0    `
07 Mar 2008, 17:05
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
"Beth EEEw"
07 Mar 2008, 17:10
bitRAKE

Joined: 21 Jul 2003
Posts: 2889
Location: [RSP+8*5]
bitRAKE
If vertical brakets can be used for cardinality of a set then how is it that |w_1^CK | is smaller than any "Beth" number? Is it because an ordinal is not the set?

Edit: think I found the answer: any countable set has cardinality aleph-1.

_________________
07 Mar 2008, 17:13
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
bitRAKE wrote:
If vertical brakets can be used for cardinality of a set then how is it that |w_1^CK | is smaller than any "Beth" number? Is it because an ordinal is not the set?

Edit: think I found the answer: any countable set has cardinality aleph-1.
Hehe, I made bitRAKE do some serious searching.
07 Mar 2008, 17:28
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
(Deleted)

Last edited by MHajduk on 07 Mar 2008, 19:15; edited 3 times in total
07 Mar 2008, 17:32
bitRAKE

Joined: 21 Jul 2003
Posts: 2889
Location: [RSP+8*5]
bitRAKE
revolution wrote:
Hehe, I made bitRAKE do some serious searching.
No, searching is easy and hardly serious - giving some conscious attention to the matter is much more difficult. Lacking a background in this material, I've used much cut-n-paste and permutations without really trying to understand.

Still ordinals seem lofty amusement with little practical use. The busy beaver though has some useful branches of discovery and applications to real world problems. Can anyone code some x86 demonstrating ordinals?

_________________
07 Mar 2008, 17:45
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
I expect you use ordinals everyday without realising it: first, second, third, etc.
07 Mar 2008, 17:49
bitRAKE

Joined: 21 Jul 2003
Posts: 2889
Location: [RSP+8*5]
bitRAKE
Thought you would have noticed my flippant style - I rarely use first, second, ... too many interruptions. Rather I mean ordinal use beyond cardinality. If all ordinal use can be replaced by cardinals then it's merely an academic abstraction (nothing wrong with that).

_________________
07 Mar 2008, 17:58
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
bitRAKE wrote:
If all ordinal use can be replaced by cardinals ...
Sure we can:

Ordinal: Who came first in the race?

Cardinal: Who was it that finished the race in position one?
07 Mar 2008, 18:04
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7712
Location: Kraków, Poland
Tomasz Grysztar
Ordinals are needed for the induction, and not replacable there.
07 Mar 2008, 18:14
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17248
revolution
The obvious flaw in my statements was "position one", which of course is the same as "first", it gives a position and thus an order.
07 Mar 2008, 18:20
bitRAKE

Joined: 21 Jul 2003
Posts: 2889
Location: [RSP+8*5]
bitRAKE
Tomasz Grysztar wrote:
Ordinals are needed for the induction, and not replacable there.
Thank you, that does make sense. How to code an inductive system, though? I see why they have all these features now and why comparison is so difficult.

_________________
07 Mar 2008, 18:37
edfed

Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
x is the bigger number, because it can be anything. from 0 to oo
07 Mar 2008, 19:41
r22

Joined: 27 Dec 2004
Posts: 805
r22
|[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.
07 Mar 2008, 21:22
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