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

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revolution
When all else fails, read the source


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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.
Glad to hear it Smile
Post 07 Mar 2008, 15:02
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MHajduk



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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). Wink

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)
Post 07 Mar 2008, 16:40
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revolution
When all else fails, read the source


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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.
Post 07 Mar 2008, 16:50
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MHajduk



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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    
Very Happy
Post 07 Mar 2008, 16:56
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revolution
When all else fails, read the source


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


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revolution
Oh I got it "Beth Ew^w".
Post 07 Mar 2008, 17:04
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MHajduk



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MHajduk
Code:
Beth_EEE0    
Post 07 Mar 2008, 17:05
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revolution
When all else fails, read the source


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revolution
"Beth EEEw"
Post 07 Mar 2008, 17:10
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bitRAKE



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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.

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


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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. Razz
Post 07 Mar 2008, 17:28
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MHajduk



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MHajduk
(Deleted)


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



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bitRAKE
revolution wrote:
Hehe, I made bitRAKE do some serious searching. Razz
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?

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Post 07 Mar 2008, 17:45
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revolution
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revolution
I expect you use ordinals everyday without realising it: first, second, third, etc.
Post 07 Mar 2008, 17:49
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bitRAKE



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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).

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


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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?
Post 07 Mar 2008, 18:04
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Tomasz Grysztar
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Tomasz Grysztar
Ordinals are needed for the induction, and not replacable there.
Post 07 Mar 2008, 18:14
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revolution
When all else fails, read the source


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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.
Post 07 Mar 2008, 18:20
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bitRAKE



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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.

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Post 07 Mar 2008, 18:37
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edfed



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edfed
x is the bigger number, because it can be anything. from 0 to oo
Post 07 Mar 2008, 19:41
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r22



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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.
Post 07 Mar 2008, 21:22
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