flat assembler
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alessandro95
Just to give an idea of how quickly consecutive R grows:
R2=11 RR2=11111111111 RRR2=~1.11*10¹¹¹¹¹¹¹¹¹¹¹ and we can define this recursevely as Rq=~1.11*10^q nRq=~1.11*10^(n1)Rq where nRq stand for R applied n times to q Imagine using G or S(k,n) as q and applies as many R as we can without using more than 9 charachters, how to decide which one is bigger? p.s. forgot to mention before but this numbers made by a string of 1s are called repunits 

05 Apr 2013, 05:33 

revolution
alessandro95 wrote: and we can define ... However I think that the growth of R will most probably be easily dwarfed by the S() function. 

11 Apr 2013, 06:20 

alessandro95
Sorry, describe was the right term, not define.
There surely are function with a much faster growth, but do they use only 1 character? I don"t know how to compare them so I was proposing the R function, althought it is probably possible to write a bigger number without breaking the 9 characters limit 

11 Apr 2013, 07:57 

r22
http://googology.wikia.com/wiki/BIG_FOOT
Quote: BIG FOOT$ http://googology.wikia.com/wiki/Rayo%27s_number Quote: Rayo(G$$) ... 

03 Feb 2015, 04:29 

revolution
How do those compare to the current list? Do they make the top 5?


03 Feb 2015, 05:10 

r22
Big Foot and Rayo, far exceed TREE() TREE sequence and SCG() Sub Cubic Graph number., which are burdened by the fact that they are computable.
FOOT  First Order Oodle Theory (as opposed to FOST  First Order Set Theory) is some conjured up augmented set theory that formalizes the abstract of this thread "the largest number that can be represented with N symbols". Using this theory the top 5 in this thread could be mere symbols used to define this number. BIG FOOT is FOOT^10(10^100), so in the realm of uncomputable numbers we could get even larger with the 9 character constraint by going with. Quote: FOOT^G(G) It's not cheating in the alternate oodleverse. 

03 Feb 2015, 16:42 

revolution
I guess that the first step is to show that a number with G symbols is larger than G itself. I think this step is trivial, so then we move on to show that FOOT(G) applied recursively G times will get progressively larger.
So far so good. But what about recursion? If we have FOOT^G(G) as the largest number in 9 characters then presumably this is larger than FOOT(G) (the largest number in G characters). So how can a 9 character value be larger than a G character value? We could just keep putting (FOOT^G(G))^(FOOT^G(G))^...^(FOOT^G(G)) to fit within G characters and we end up with a infinite selfreferential loop. 

04 Feb 2015, 08:55 

gens
888888888


05 Feb 2015, 01:07 

revolution
gens wrote: 888888888 

05 Feb 2015, 01:25 

r22
revolution wrote: I guess that the first step is to show that a number with G symbols is larger than G itself. I think this step is trivial, so then we move on to show that FOOT(G) applied recursively G times will get progressively larger. From my rudimentary ?mis?understanding of first order set theory: a self referencing recursion would just be considered infinity and wouldn't be used within our domain of large theoretical numbers. Also terms must be obtainable through a finite application of variable and function rules, so eventually we'd be forced to use a symbol that didn't branch out into more self referencing symbols. At what stage this happens is, I guess, what makes the result finite but still uncomputable. I'm also selling magic text (.txt) files that keep monsters away, but only on floppy disk. 

05 Feb 2015, 16:16 

revolution
And the infinity is only of Aleph0 class so it wouldn't even make the top5 transfinite list either.


05 Feb 2015, 16:26 

typedef
∞^∞^∞^∞^∞
Did I win a star? 

08 Feb 2015, 05:06 

revolution
typedef wrote: ∞^∞^∞^∞^∞ typedef wrote: Did I win a star? 

08 Feb 2015, 05:15 

l4m2
9[9]9
maxnumber(haha) 

12 Feb 2015, 10:35 

l4m2
maxhere+9


12 Feb 2015, 10:38 

revolution
l4m2 wrote: maxhere+9 However, you are welcome to try again. 

12 Feb 2015, 11:04 

l4m2
revolution wrote:
So what about 9[9[9]9]9, a[n+1]b=a[n]a[n]a[n]a(b a's) a[0]b=a+1 

12 Feb 2015, 12:06 

l4m2
revolution wrote:
Also I don't think a define all from self can be or that'd be much better: X I can let it be any number just I like to for example 10000...000(the simpliest one,but because of the tiny harddisk ) 

12 Feb 2015, 12:11 

revolution
If you read this whole thread you will see that people defining their own terms was not permitted. This if for the exact reason you mention, because any arbitrary definition could be anything, which would make the whole thing boring.


12 Feb 2015, 12:24 

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