## My number is bigger?

For all your silly time-killing forum games.

Moderators: jestingrabbit, Moderators General, Prelates

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

Technically phillip's number isn't well-defined, because he never defined "->->->->".

But yeah, given the most natural definition, his last number is about [w+3]1000, which is a bit bigger than mine (M3=[w+3]10) but much much smaller than 10ls's (which is something like [w^2]12=N12=[12,0]10).

And since we're already beyond the limit of [a,b]c , I'll define arbitrary-length arrays:

1. [anything]1=10
2. n=10n
3. [0,...,0,a,...,n]m = [a,...,n]m
4. [a,b,c,...,n+1](m+1) = [a,b,c,...,n][a,b,c,...,n+1]m
5. [a,b,n+1,(k zeros)]m = [a,b,n,m,(k-1) zeros]m
6. Nn = [1,0,0]n ; Pn = [1,(n zeros)]10

Also, for finer tuning of my numbers, I define a binary version of P for selected rational numbers:

7. For integers n>1, 10n<=m<10n+1: (m/10n)Pn = [the digits of m seperated by commas]10

And submit this entry:

1.23P2 = (123/100)P2 = [1,2,3]10 = [w^2+w*2+3]10

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

s(10,10,1,1,3)
mom fapathi

solune
Posts: 121
Joined: Thu Jul 21, 2011 12:58 pm UTC

### Re: My number is bigger?

I've completely lost the plot for a few posts now, so I'll just say s(10,10,1,4) and hope it means anything to anyone.

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

Too small. Also try to include fgh levels if you can
mom fapathi

solune
Posts: 121
Joined: Thu Jul 21, 2011 12:58 pm UTC

### Re: My number is bigger?

oh I meant s(10,10,1,1,4)

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

https://stepstowardinfinity.wordpress.com/array/extended/ definition

I'm putting s(10,10{2}2)
fgh level is about w^w
mom fapathi

SuperJedi224
Posts: 16
Joined: Thu Apr 16, 2015 4:19 pm UTC

### Re: My number is bigger?

In Cascading-E Notation, my next number is E100#^#2#2, or approximately f[w^w](f[w](100)).

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

s(10,10{3}2)

fgh level is w^w^2
mom fapathi

phillip1882
Posts: 145
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: My number is bigger?

Ackermann( Ackerman(1000,Ackerman(1000,Ackermann(1000,1000))),Ackermann(100->->100,100->->100))
good luck have fun

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

Too small, only has a level of w^2
mom fapathi

phillip1882
Posts: 145
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: My number is bigger?

okay, not quite sure how you're determining that, but ill take your word for it.

Tree(Tree(Tree(10000000->->->->->10000000)))
good luck have fun

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

The OP gave the level as w^2 because he mistakenly thought you're using Conway Chained Arrows. In that notation, a->...->a (with a arrows) is indeed on that level.

With your notation, I'm afraid the final result is much smaller.

I'll actually show you how I figured this out:

We do this by counting the levels of recursion in the notation. A "level of recursion" is every time you've taken the previous function and nested it n times:

a+b : level 1
a++b: level 2 (level 1 repeated b times)
a+++b: level 3 (level 2 repeated b times)
a++++b: level 4 (level 3 repeated b times)

and so on.

Then we have:

a->b->c = a++++...+++++b

We call this "level w", because it contains all the finite levels within itself. Think of "w" as a wildcard that can be replaced by any finite number. For a fixed value of c, a->b->c would be at level c, and since c can be as large as we want it to be, a->b->c corresponds to level w.

and then you've written

a->->b = a->a->...->a (b times)

Which is "level w" repeated b times, so we add one to the level of a->b->c and get w+1.

And that's it.

The Ackerman, which is merely an w-level function, doesn't change the final result by much. So the end result is still an w+1 function.

Back to your notation, we can continue with
a->->->b = a->->a...->->a : w+2 ("w+1"-level repeated b times)

a->->->->b = a->->->a...->->->a : w+3 ("w+2"-level repeated b times)

and so on.

This last expression is why I estimated your previous number of 100->->->->100 as roughly [w+3]100.

We could continue, adding another "->" for every level, and then we could do something like this:

a&b = a->->...->a (with b ->'s)

This is as powerful as w+b for arbitrary large b. Once again we need a "wildcard" here, so we replace that b with an w and get w+w=w*2 for a&b

Doing all of this again with the "&'s" we can get:

a&&b = a&a&a&...&a (level w*2+1)
a&&&b = a&&a&&a&&...a (level w*2+2)

and so on, until we have (say):

a@b = a&&....&&b (with b &'s)

which would be level w*2+w = w*3.

At this point, the pattern is clear, but we need to constantly come up with new symbols. So why not use numbers, instead of symbols? We can write  instead of "+" and  instead of "->" and  instead of "&" and  instead of "@", and voila! We have an a system with an infinite number of symbols!

So now:

ab = a->b is level w
ab = a&b is level w*2
ab = a@b is level w*3
ab is level w*4
and so on.

Now the function a[n]b has strength of w*n, where n is an arbitrary large number. So we replace the "n" with an "w" and we get w*w = w^2.

And this is, basically, what Conway Chained Arrows do. If you look carefully at the expansion rules for Conway Arrows, you will see that every additional arrow adds another w levels. The final number in the chain (regardless of its length) serves as a level counter within every set of w levels.

Of-course, we are way beyond this now. Which brings me to your last entry:
Tree(Tree(Tree(10000000->->->->->10000000)))

By now you should know that "10000000->->->->->10000000" is only at level w+4, so that's nothing exciting at this point.

However, "Tree" is a very fast growing-function. In term of ordinals level, TREE is way beyond anything we can describe with w's. It's roughly at a level called "The Small Veblen Ordinal" (SVO) which is way too large for me to explain exactly how it works right now.

In short, even writing Tree(3) would have been a winner at this point. On the other hand, by nesting Tree into itself, you haven't really increased the number by much. If the ordinal level of Tree(n) is X, then the ordinal level of Tree(Tree(...(Tree(n))...)) is merely X+1.
Last edited by PsiCubed2 on Tue May 21, 2019 10:27 am UTC, edited 4 times in total.

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

As for my own number, I'll use a variant of pair sequences:

Rules:

(1) Expressions are of the form (a1,b1)(a2,b2)...(ak,bk)[n]
(2) If k=1 then the expression evaluates to n+1.
(3) If ak=0 then we delete the final pair and add 1 to n.
(4) If ak>0 and bk=0 then we do the following:
(4-i) We look for the rightmost pair (ai,bi) such that ai<ak. If no such pair is found, we set i=1.
(4-ii) We delete the final pair (ak,bk)
(4-iii) We append n-1 additional copies of (ai,bi)...(ak-1,bk-1) just before the [n]
(4-iv) The value of n remains unchanged.
(5) If ak>0 and bk>0 then we do the following:
(5-i) We look for the rightmost pair (ai,bi) such that:
(5-i-1) ai<ak.
(5-i-2) bi<bk.
(5-i-3) For every j>i, ai<aj
If no such pair is found, we set i=1
(5-ii) We set c=ak-ai
(5-iii) We delete the final pair (ak,bk)
(5-iv) For all numbers K from 1 to n-1 we do the following:
(5-iv-1) Insert (ai+K*c,bi)...(ak-1+K*c,bk-1) just before the [n]
(5-v) The value of n remains unchanged.

And my number:

(0,0)(1,1)(2,1)(3,1)(4,1)(0,0)(1,0)(1,0) ~ [LVO]1032 >> TREE(anything reasonable)

(should be around TE32 in my letter notation, if I ever define it up to those levels)

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

https://stepstowardinfinity.wordpress.c ... ti-expand/

My number is s(10,10{1``2}2) (around BHO level)

Also, no uncomputables
mom fapathi

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

### Re: My number is bigger?

10^50+( ( 2^^^( s(10,10{1``2}2) ) )

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

(0,0)(1,1)(2,2)(1,1)(0,0)(1,0)(1,0) ~ [εBHO+1](1032)

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

s(10,10{1``1``2}2) ~ psi(W_2^2)
mom fapathi

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

### Re: My number is bigger?

X(s(10,10{1``1``2}2) ~ psi(W_2^2)) where X() is the s()th integral of s()

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

stop making naive extensions
mom fapathi

Daggoth
Posts: 52
Joined: Wed Aug 05, 2009 2:37 am UTC

### Re: My number is bigger?

s(20,30{2``3``3}3

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

>:C
s(10,10{1{2^``}2}2)
mom fapathi

solune
Posts: 121
Joined: Thu Jul 21, 2011 12:58 pm UTC

### Re: My number is bigger?

Just to make lllllllllwith10ls angry:

s(10,10{1{2^``}2}2) + 1

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

s(10,10{1{2^``}2}2)+4
mom fapathi

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

Loader's Number.

Definition:
Spoiler:
The output of the following program in C, assuming int variables that never overflow:

#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T L X C
S (v+2, t U y C c, Z (X )))
:
A (T L X C
T Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B c = P d, c C
t U t C
u U u) )
C
c && B
t = P
~u & 2 | B
u = 1 << P L c C u) C
P L c C t) C
c = r C
u / 2 & B
c = P t, c C
u U t C
t = 9 );
R a = P P t, P u, P x, c)) C
a F
}
main ()
R D (D (D (D (D (99)))) F

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

god dammit
mom fapathi

Meowers
Posts: 6
Joined: Wed Apr 06, 2016 1:35 am UTC

### Re: My number is bigger?

Loader's number+1

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

The output of the Loader's program, when we replace the "99" with "100" "999" (just to be on the safe side)

username5243
Posts: 49
Joined: Thu Jun 25, 2015 10:43 am UTC
Location: None of your business

### Re: My number is bigger?

The output of the Loader's number program when 99 is changed to Loader's Number

...this is going nowhere...
This is a signature, in case you didn't notice.

PsiCubed2
Posts: 17
Joined: Tue Apr 02, 2019 8:55 pm UTC

### Re: My number is bigger?

Are you going to answer my PM?

Meowers
Posts: 6
Joined: Wed Apr 06, 2016 1:35 am UTC

### Re: My number is bigger?

That plus Loader's number multiplied by 10^1000

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

Define D(x) to be the output of the Loader function where 99 is changed to x.

My number is d(3,3{1,,,3}2) where d(#) is s(#) in strong array notation but the base rule is changed to D(a*b) instead of a^b. Definition of strong array notation: https://stepstowardinfinity.wordpress.com/array/drop/sec-drop/
mom fapathi

username5243
Posts: 49
Joined: Thu Jun 25, 2015 10:43 am UTC
Location: None of your business

### Re: My number is bigger?

Salad numbers are bad... just saying.

If D is loader's function (D^5(99) is Loader's number), then I'll go:

D^Loader's Number(99)

(Yes, that's not much better than the last few. But no idea how to get out of this loop.)
This is a signature, in case you didn't notice.

lllllllllwith10ls
Posts: 15
Joined: Thu Mar 07, 2019 2:52 am UTC

### Re: My number is bigger?

D^(D^(loaders number)(99))(99)
mom fapathi

Return to “Forum Games”

### Who is online

Users browsing this forum: No registered users and 25 guests