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Author
alessandro95

Joined: 24 Mar 2013
Posts: 62
alessandro95
Rn¹º is the base-10 number made by n 1s in a row, e.g.
R5¹º=11111

(actually n should be a subscript but looks like it cannot be shown on this forum)
conventionally if the base is 10 then the can be omitted.

I don't know what is bigger between the S(k,n) function proposed by bitRAKE or Graham's number but

RG

where G is graham number

and

RS(k,n)

are both way bigger than G and S(k,n) respectively, and we have some.characters.left to make them even bigger (something like RRRRRRRRG, imagine every letter as subscript of the preceding one is a number absurdely huge)
05 Apr 2013, 05:17
alessandro95

Joined: 24 Mar 2013
Posts: 62
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^(n-1)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
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
alessandro95 wrote:
and we can define ...
It doesn't seem to follow the arbitrary rules we have used for this thread. Defining our own functions was not allowed.

However I think that the growth of R will most probably be easily dwarfed by the S() function.
11 Apr 2013, 06:20
alessandro95

Joined: 24 Mar 2013
Posts: 62
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

Joined: 27 Dec 2004
Posts: 805
r22
03 Feb 2015, 04:29
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
How do those compare to the current list? Do they make the top 5?
03 Feb 2015, 05:10
r22

Joined: 27 Dec 2004
Posts: 805
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 un-computable 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
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
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 self-referential loop.
04 Feb 2015, 08:55
gens

Joined: 18 Feb 2013
Posts: 161
gens
888888888
05 Feb 2015, 01:07
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
gens wrote:
888888888
I am confident that there are already larger numbers given in this thread.
05 Feb 2015, 01:25
r22

Joined: 27 Dec 2004
Posts: 805
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.

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 self-referential loop.

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 un-computable.

I'm also selling magic text (.txt) files that keep monsters away, but only on floppy disk.
05 Feb 2015, 16:16
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
And the infinity is only of Aleph-0 class so it wouldn't even make the top-5 trans-finite list either.
05 Feb 2015, 16:26
typedef

Joined: 25 Jul 2010
Posts: 2913
Location: 0x77760000
typedef
∞^∞^∞^∞^∞

Did I win a star?
08 Feb 2015, 05:06
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
typedef wrote:
∞^∞^∞^∞^∞
You either didn't read the rules, or you ignored the rules, so your submission in not accepted.
typedef wrote:
Did I win a star?
Sure, you win Jack Black. Have fun with your new star.
08 Feb 2015, 05:15
l4m2

Joined: 15 Jan 2015
Posts: 648
l4m2
9[9]9
maxnumber(haha)
12 Feb 2015, 10:35
l4m2

Joined: 15 Jan 2015
Posts: 648
l4m2
maxhere+9
12 Feb 2015, 10:38
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
revolution
l4m2 wrote:
maxhere+9
This was already tried in a variant form by Goplat. And it was subsequently shown to be unworkable and thus disallowed.

However, you are welcome to try again.
12 Feb 2015, 11:04
l4m2

Joined: 15 Jan 2015
Posts: 648
l4m2
revolution wrote:
l4m2 wrote:
maxhere+9
This was already tried in a variant form by Goplat. And it was subsequently shown to be unworkable and thus disallowed.

However, you are welcome to try again.

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

Joined: 15 Jan 2015
Posts: 648
l4m2
revolution wrote:
l4m2 wrote:
maxhere+9
This was already tried in a variant form by Goplat. And it was subsequently shown to be unworkable and thus disallowed.

However, you are welcome to try again.

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
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17270
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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