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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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revolution
r22 wrote:
So the largest possible number in 9 ASCII characters is ...
Code:
S_ZM(K_i) or ZM^S(K_i) in think the latter syntax is more obvious    
Do you have a reference source for this notation?
Post 17 Mar 2008, 01:28
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r22



Joined: 27 Dec 2004
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r22
I don't think notation for hypothetical Turing machine step counting on program input exists.

So its in the same article as bitRAKE's G-cube notation.
Post 17 Mar 2008, 19:58
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sleepsleep



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sleepsleep
if i ask this question to God,
"what is the largest/smallest number"

what answer i would get?
Post 08 May 2009, 12:15
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bitshifter



Joined: 04 Dec 2007
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bitshifter
Can we use base 36 numbering system?

Z^Z^Z^Z^Z

Thats pretty damn big if you ask me.
Post 08 May 2009, 12:23
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revolution
When all else fails, read the source


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revolution
Shocked this topic again! Hehe, "Z^Z^Z^Z^Z", sorry not even close to the previous answers given. But you are welcome to keep trying.
Post 08 May 2009, 12:29
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Borsuc



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Borsuc
sleepsleep wrote:
if i ask this question to God,
"what is the largest/smallest number"

what answer i would get?
Abnormal Program Termination. Please file all bugs encountered to god@universe.com.

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Post 08 May 2009, 21:24
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Tomasz Grysztar
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Tomasz Grysztar
Borsuc wrote:
Abnormal Program Termination. Please file all bugs encountered to god@universe.com.
Doesn't he use any JIRA or something? Wink
Post 08 May 2009, 21:27
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Borsuc



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Borsuc
I think the number overflowed. Not sure if God debugs anything though. Even if He did, we would also get a 'modification' to our brains so it's like it didn't happen Razz
Post 08 May 2009, 21:34
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sleepsleep



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sleepsleep
probably God says.
my biggest number is what the biggest number you could think of plus 1.

hahaha
Post 08 May 2009, 21:46
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pal



Joined: 26 Aug 2008
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pal
How about something like:

TREE(GG$)

or

TREE(G^G)

Code:
http://en.wikipedia.org/wiki/Kruskal%27s_theorem#Friedman.27s_finite_form    
Post 09 May 2009, 10:17
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revolution
When all else fails, read the source


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revolution
pal wrote:
TREE(G^G)
Very nice. Now how to determine if this is larger than S^S(G)(G) ??

Maybe also G^TREE(G)? But I think that is likely to be smaller than pal's suggestion.

How about TREE(S(G)) Wink Razz 10 characters! Ha! fooled you.

The TREE sequence begins TREE(1) = 1, TREE(2) = 3, then suddenly TREE(3) explodes to a value so enormously large that many other "large" combinatorial constants, such as Friedman's n(4), are "completely unnoticeable" by comparison. A lower bound for n(4), and hence an extremely weak lower bound for TREE(3), is A(A(...A(1)...)), where the number of A's is A(187196), and A() is a version of Ackermann's function: A(x) = 2↑↑...↑x with x-1 ↑s (Knuth up-arrows). Graham's number, for example, is "unnoticeable" even in comparison to this "unnoticeable" lower bound for TREE(3).
Post 09 May 2009, 10:54
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pal



Joined: 26 Aug 2008
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pal
I'm not sure how you would do the comparison. Very large numbers as such is a new realm for me.

Not sure if this will be bigger:

G^A(GG,G)

Or some permutation of that.

Code:
http://en.wikipedia.org/wiki/Ackermann_function    
Post 09 May 2009, 11:28
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revolution
When all else fails, read the source


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revolution
We already covered the Ackermann function previously. The Busy Beaver (BB) function (and related S()) grows faster than Ackermann.

Now we just have to show whether or not TREE(G^G) > S^S(G)(G). That could be tricky to do!
Post 09 May 2009, 11:32
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pal



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pal
My bad, I thought you did, but I posted it anyway. Time to do some Googling.
Post 09 May 2009, 11:34
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revolution
When all else fails, read the source


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revolution
BTW: Is G$$ > G^G Question
Post 09 May 2009, 11:35
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revolution
When all else fails, read the source


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revolution
Also: Just to remind new-comers to this thread that S^S(G)(G) means: S(S(S(S...S(G)))) with an S(G) count of recursive S(..) levels.

And S() is the Max shifts function.

And G is Graham's number.
Post 09 May 2009, 11:39
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pal



Joined: 26 Aug 2008
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pal
One interesting one would be. You could have:

tan89.(9)

(9) means 999... But then that wont work as it would be oo as 89.999... = 90, tan(90) is infinite.

Code:
http://en.wikipedia.org/wiki/0.999...    


The hyperbolic cosine and sine functions (cosh and sinh) can produce massive numbers), but not as big as some already stated.

Some reading:

Code:
http://www.math.ohio-state.edu/~friedman/pdf/EnormousInt.12pt.6_1_00.pdf    
Post 09 May 2009, 11:56
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manfred



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manfred
My answers:
very huge ;second place
largest ;first place
It's only a joke, however...

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Sorry for my English...
Post 09 May 2009, 22:56
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edemko



Joined: 18 Jul 2009
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edemko
(0x7e-0x20+0x01)^9
Post 30 Dec 2009, 23:29
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revolution
When all else fails, read the source


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revolution
serfasm wrote:
(0x7e-0x20+0x01)^9
18 characters. Too long. And not very big anyway.
Post 31 Dec 2009, 02:40
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