A new my number is bigger

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Meowers
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Re: A new my number is bigger

Postby Meowers » Sun Jan 21, 2018 7:44 pm UTC

5|3|5

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Sun Jan 21, 2018 8:43 pm UTC

5|5|5 = (10↑↑↑↑↑)25

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Meowers
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Re: A new my number is bigger

Postby Meowers » Mon Jan 22, 2018 12:37 am UTC

6|2
(=5|5|10)

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Mon Jan 22, 2018 1:20 am UTC

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

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

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Meowers
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Re: A new my number is bigger

Postby Meowers » Mon Jan 22, 2018 4:10 am UTC

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

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Marki
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Re: A new my number is bigger

Postby Marki » Mon Jan 22, 2018 10:48 am UTC

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

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Meowers
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Re: A new my number is bigger

Postby Meowers » Tue Jan 23, 2018 2:14 am UTC

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

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Tue Jan 23, 2018 11:45 am UTC

J6 = 10↑↑↑↑↑↑10

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Meowers
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Re: A new my number is bigger

Postby Meowers » Tue Jan 23, 2018 6:38 pm UTC

J7=10{7}10

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Tue Jan 23, 2018 8:09 pm UTC

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

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Marki
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Re: A new my number is bigger

Postby Marki » Wed Jan 24, 2018 12:25 pm UTC

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

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Wed Jan 24, 2018 1:26 pm UTC

{8,8,8}

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Meowers
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Re: A new my number is bigger

Postby Meowers » Sun Jan 28, 2018 11:09 pm UTC

K1.9=JJ0.9~J7.93

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Mon Jan 29, 2018 7:08 am UTC

I thought you wanted to speed up?

fω(9)

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Meowers
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Re: A new my number is bigger

Postby Meowers » Wed Jan 31, 2018 8:25 pm UTC

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

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Thu Feb 01, 2018 7:24 pm UTC

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

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Marki
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Re: A new my number is bigger

Postby Marki » Sat Feb 03, 2018 3:24 am UTC

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

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Sat Feb 03, 2018 4:42 pm UTC

4→2→2→2

Daggoth
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Re: A new my number is bigger

Postby Daggoth » Thu Feb 08, 2018 3:42 am UTC

6^(4→2→2→2)

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Re: A new my number is bigger

Postby Simply Beautiful Art » Sun Feb 11, 2018 5:46 pm UTC

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
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Re: A new my number is bigger

Postby PsiSquared » Mon Feb 12, 2018 12:04 pm UTC

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
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Re: A new my number is bigger

Postby Simply Beautiful Art » Tue Feb 13, 2018 11:51 am UTC

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

Spoiler:
~ 34↑³²34

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Tue Feb 13, 2018 7:40 pm UTC

K(181/4)
Spoiler:
~10↑3464

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Meowers
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Re: A new my number is bigger

Postby Meowers » Tue Feb 13, 2018 7:53 pm UTC

10↑100010

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Tue Feb 13, 2018 8:16 pm UTC

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

Simply Beautiful Art
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Re: A new my number is bigger

Postby Simply Beautiful Art » Tue Feb 13, 2018 9:50 pm UTC

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

Spoiler:
≈ fω+1(4) ≈ g4

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Wed Feb 14, 2018 7:51 am UTC

Whoa! You're taking no prisoners, eh?

Well then:

22→22→22→2

Spoiler:
~ K22 ~ fω+1(22)

Simply Beautiful Art
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Re: A new my number is bigger

Postby Simply Beautiful Art » Wed Feb 14, 2018 12:08 pm UTC

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

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Meowers
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Re: A new my number is bigger

Postby Meowers » Sat Feb 17, 2018 5:40 pm UTC

g64=Graham's number

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emlightened
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Re: A new my number is bigger

Postby emlightened » Sun Feb 18, 2018 12:42 am UTC

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."

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emlightened
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Re: A new my number is bigger

Postby emlightened » Sun Feb 18, 2018 12:44 am UTC

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
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Re: A new my number is bigger

Postby Simply Beautiful Art » Sun Feb 18, 2018 3:55 pm UTC

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

Simply Beautiful Art
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Re: A new my number is bigger

Postby Simply Beautiful Art » Sun Feb 18, 2018 3:57 pm UTC

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

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

PsiSquared
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Re: A new my number is bigger

Postby PsiSquared » Sun Feb 18, 2018 6:11 pm UTC

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

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

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emlightened
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Re: A new my number is bigger

Postby emlightened » Sun Feb 18, 2018 8:08 pm UTC

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
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Re: A new my number is bigger

Postby Simply Beautiful Art » Mon Feb 19, 2018 1:20 am UTC

... 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
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Re: A new my number is bigger

Postby Simply Beautiful Art » Mon Feb 19, 2018 1:22 am UTC

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

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emlightened
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Re: A new my number is bigger

Postby emlightened » Mon Feb 19, 2018 9:44 am UTC

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

Postby Simply Beautiful Art » Mon Feb 19, 2018 2:06 pm UTC

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
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Re: A new my number is bigger

Postby PsiSquared » Mon Feb 19, 2018 2:38 pm UTC

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)


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