## A new my number is bigger

For all your silly time-killing forum games.

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

### Re: A new my number is bigger

5|3|5

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

5|5|5 = (10↑↑↑↑↑)25

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

### Re: A new my number is bigger

6|2
(=5|5|10)

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

6|2 is 5|10 rather than 5|5|10.
(10↑↑↑↑↑↑2 = 10↑↑↑↑↑10)

So the current "champion" is still my 5|5|5.

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

### Re: A new my number is bigger

6|3
(=5|5|5|1=5|5|10)

Marki
Posts: 5
Joined: Sun Oct 22, 2017 3:23 am UTC
Contact:

### Re: A new my number is bigger

10↑↑↑↑↑10↑↑↑↑↑10↑↑10
I like big big big big big numbers.

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

### Re: A new my number is bigger

6|4
We need to get to FGH w at some point...

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

J6 = 10↑↑↑↑↑↑10

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

### Re: A new my number is bigger

J7=10{7}10

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

3→2→2→2
Spoiler:
≈ [1,1,1,1,1,1,1 ; 13]
≈ J7.11

Marki
Posts: 5
Joined: Sun Oct 22, 2017 3:23 am UTC
Contact:

### Re: A new my number is bigger

J7.15
I like big big big big big numbers.

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

{8,8,8}

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

### Re: A new my number is bigger

K1.9=JJ0.9~J7.93

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

I thought you wanted to speed up?

fω(9)

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

### Re: A new my number is bigger

K2=J10=10{10}10={10,10,10}=(10)|10=(11)|2

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

11111111111↑↑↑↑↑↑↑↑↑↑↑11111111111
(ׂ11 1's, 11 ↑'s, 11 1's)

Marki
Posts: 5
Joined: Sun Oct 22, 2017 3:23 am UTC
Contact:

### Re: A new my number is bigger

(10^10)↑↑↑↑↑↑↑↑↑↑↑↑(10^10)
I like big big big big big numbers.

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

4→2→2→2

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

### Re: A new my number is bigger

6^(4→2→2→2)

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

Let (a,b,c) be an ordered triplet.

Define T as follows:
T(0) = {0}
T(n+1) = {0,...,n+1} ∪ {(a,b,c) : a,b,c ∈ T(n)}
T = ⋃T(n), n ∈ N the set of naturals

Let H : TxN → N and R : TxN → T be recursive functions defined as follows:

H(1,n) = n
H(a,n) = H(R(a,n),n+1), a ≠ 1
R(0,n) = n
R(k,n) = k-1, k ∈ N-{0}
R((a,1,c),n) = a
R((a,b,1),n) = a
R((a,b,c),n) = ((a,b,R(c,n)),R(b,n),a), b and c ≠ 1

My number is H((0,4,1),17).

Spoiler:
Approximately (18↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑18)↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑18

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

Define:

a<1>b = a^b
a<n+1>1 = a
a<n+1>(b+1) = a<n>(a<n+1>b)

My number is 11<22>33
Spoiler:
11↑2233 ~ J22

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

My number is H((0,4,1),33)

Spoiler:
~ 34↑³²34

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

K(181/4)
Spoiler:
~10↑3464

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

### Re: A new my number is bigger

10↑100010

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

2→22→2→2
Spoiler:
= 2↑419430422 ~ JE6.6

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

H((0,3,(0,1,1)),1)

Spoiler:
≈ fω+1(4) ≈ g4

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

Whoa! You're taking no prisoners, eh?

Well then:

22→22→22→2

Spoiler:
~ K22 ~ fω+1(22)

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

No, it's actually that my notation is slightly jumpy at some values.

H((0,3,(0,1,1)),15)

Spoiler:
~ fω+1(32) ~ g32

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

### Re: A new my number is bigger

g64=Graham's number

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: A new my number is bigger

Hi.

I'm gonna introduce something I'm gonna call basket notation. Procedure in bold.

You have a series of baskets, which contain numbers, all followed by a number.

Like this: [2][5][1][1]3

You then look at the last basket that doesn't have a 0 in and decrease the number in that basket (if it's the first basket and becomes a 0, delete it). If there are any baskets after this one, then put the number at the end in each of those. Lastly, decrease the final number. Like this:

[2][5][1][1]3
[2][5][1][0]4
[2][5][0][4]5
[2][5][0][3]6
[2][5][0][2]7
[2][5][0][1]8
[2][5][0][0]9
[2][4][9][9]10
[2][4][9][8]11
...
[1][0][0][0]a
[a][a][a]a+1
...

Repeat until you get a single number.

Now, as it is, this would get us up to level ω. So, we take the most sensible answer, which is basket-ception.

Now, a basket doesn't look like this: [a]

But like this: [a] or [a[_]] or [a[_][_]] or etc. The [_] ones are called balnk baskets.

Now, what about when the rightmost basket with a nonzero number contains other (not nested) baskets? In that case, make <end number> copies of the basket (but with a blank basket removed) and put them immediately to the right of the basket in question, with the number in these baskets and all baskets to the right replaced with the number on the end.

Like this:

[4[_][_]]1
[3[_][_]][1[_]][1[_]]2
[3[_][_]][1[_]][0[_]][2][2]3
...
[3[_][_]][1[_]][0[_]][0][0]23
[3[_][_]][0[_]][23][23]...[23][23][23[_]][23][23]23
...

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: A new my number is bigger

Number:

[100][75[_]][50]25 ~ g100

Feel free to ask clarifying questions.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

To be clear, [2][0[_]]3 = [1][3[_]]4?

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

H((0,3,((0,1,1),1,1)),3)

Spoiler:
~ fω+2(3) ~ gg[sub]g[sub]3[/sub][/sub]

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

Are you sure that's the number you wanted to send?

It looks like it's much larger then g100...

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: A new my number is bigger

Does it?

It looks to me like [e][d][c][b][0]a is about Hω4e+ω3d+ω2c+ωb(a), and like [a][b[_]]10 is about Hωω+1b+ωωa(10) ~ gb. No function iteration is used, so the notation works at hardy hierarchy levels, as opposed to FGH levels.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

... like [a][b[_]]10 is about Hωω+1b+ωωa(10)...

To me it looks like [a][b[_]]10 ~ Hωω+1a+ωωb(10), certainly we agree the b gets used up before the a does?

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

Either being the case, your number is a tad larger than you claim. Approximating [a][b[_]]10 as fω+2(a) tells us so.

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
Location: Somewhere cosy.

### Re: A new my number is bigger

Yep, [2][0[_]]3 = [1][3[_]]4

That would be a typo.

And yeah, forgive my disorientation, that looks right.

[7][5[_]]3 = [7][4[_]][0][0][0]2↑(70+270+21180591620717411303494)-1 ~ fω+17(fω4(2↑2↑2↑2↑70))

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

Simply Beautiful Art
Posts: 5
Joined: Sat Feb 10, 2018 2:21 pm UTC

### Re: A new my number is bigger

H((0,4,((0,1,1),1,1)),100)

Spoiler:
~ fω+2(200)
Last edited by Simply Beautiful Art on Mon Feb 19, 2018 8:48 pm UTC, edited 1 time in total.

PsiSquared
Posts: 126
Joined: Wed May 09, 2012 6:02 pm UTC

### Re: A new my number is bigger

Whoa! Did you just jump from [ω+1]64 to [ω+2]8 ?

Assuming that's legal:

LEFT1

Spoiler:
LEFT1 = LEF10 = LF11 ~ f<sub>ω+2</sub>(10↑↑11)