My Number is Bigger! (again)

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username5243
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My Number is Bigger! (again)

Postby username5243 » Thu Jun 25, 2015 9:43 pm UTC

This is another version of the "My Number is Bigger!" thread. Here are the rules:
Your number must be bigger than the last number
Your number must be finite (FGH ordinals are allowed, but only if used in the FGH)
Uncomputable numbers are allowed, so long as you can prove they are bigger.
Also, try not to go too big too fast. Jumping from a function of order w to one of order w^w is probably not recommended. This is more a suggestion than a rule.

I'll start:
0
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patzer
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Re: My Number is Bigger! (again)

Postby patzer » Thu Jun 25, 2015 9:50 pm UTC

0.000000000000000000000000000000000020000000000000000018923
If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family Anatidae on our hands. –Douglas Adams

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Re: My Number is Bigger! (again)

Postby Vytron » Thu Jun 25, 2015 9:56 pm UTC

0.000000000000000000000000000000000020000000000000000018923
000000000000000000000000000000000020000000000000000018923
(without line breaks)

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Re: My Number is Bigger! (again)

Postby username5243 » Thu Jun 25, 2015 10:01 pm UTC

1/10^50
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Re: My Number is Bigger! (again)

Postby phillip1882 » Thu Jun 25, 2015 10:05 pm UTC

1
good luck have fun

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Re: My Number is Bigger! (again)

Postby username5243 » Thu Jun 25, 2015 10:06 pm UTC

Ooh! We have a speedy!

sqrt(6)/2
about 1.225
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Re: My Number is Bigger! (again)

Postby Vytron » Thu Jun 25, 2015 10:14 pm UTC

1+1/3

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Re: My Number is Bigger! (again)

Postby username5243 » Thu Jun 25, 2015 11:06 pm UTC

sqrt(2) ~ 1.414
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Re: My Number is Bigger! (again)

Postby Vytron » Thu Jun 25, 2015 11:17 pm UTC

(pi-3)*10

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Re: My Number is Bigger! (again)

Postby username5243 » Thu Jun 25, 2015 11:22 pm UTC

3^(1/3)

about 1.442
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Re: My Number is Bigger! (again)

Postby quintopia » Thu Jun 25, 2015 11:56 pm UTC

3830101^(1/41)

(1.447)

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Re: My Number is Bigger! (again)

Postby username5243 » Fri Jun 26, 2015 12:00 am UTC

How did you find a number that close, with a formula like that?

1.45
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Re: My Number is Bigger! (again)

Postby phillip1882 » Fri Jun 26, 2015 1:11 am UTC

10
good luck have fun

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Re: My Number is Bigger! (again)

Postby username5243 » Fri Jun 26, 2015 1:20 am UTC

10.000001
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Re: My Number is Bigger! (again)

Postby Vytron » Fri Jun 26, 2015 4:20 am UTC

username5243 wrote:How did you find a number that close, with a formula like that?


I wonder if it's "a formula like that" or trial and error (I could get arbitrarily close to a number by trial and error on the other thread.)

10.00000100000000001

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Re: My Number is Bigger! (again)

Postby patzer » Fri Jun 26, 2015 4:25 am UTC

10.10101010101
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Re: My Number is Bigger! (again)

Postby Vytron » Fri Jun 26, 2015 4:27 am UTC

10.11011011011011011

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Re: My Number is Bigger! (again)

Postby phillip1882 » Fri Jun 26, 2015 10:14 am UTC

100
good luck have fun

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Re: My Number is Bigger! (again)

Postby username5243 » Fri Jun 26, 2015 1:13 pm UTC

101
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Re: My Number is Bigger! (again)

Postby Vytron » Fri Jun 26, 2015 8:59 pm UTC

1010

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 12:49 am UTC

1100
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 11:59 am UTC

1101

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 12:10 pm UTC

1110
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 12:47 pm UTC

1111

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 12:49 pm UTC

1250
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 12:55 pm UTC

Well, the rules don't disallow referrencing other numbers on the thread, so I'll define:

f(n)=n+x

Where:

x = the second number posted on the thread.

(x=0.000000000000000000000000000000000020000000000000000018923)

Send:

f(1250)

(that is, 1250.000000000000000000000000000000000020000000000000000018923)

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 1:03 pm UTC

1251
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 1:10 pm UTC

Define:

n. (i.e. any number followed by a .) as f(n)

Send

1251.

(1251.=f(1251)=
1251.000000000000000000000000000000000020000000000000000018923)

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 1:15 pm UTC

I didn't, because if we could, we technically couldn't reference 1 or 10.

I'll introduce the FGH:
f0(n) = n+1
f1(n) = f0(f0(f0(...f0(n)...))) with n nestings = 2n

that's all we nead right now.

submit f1(626) = 1252
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 2:20 pm UTC

I introduce my Unreadable Notation, because for some reason, people find it unreadable no matter how I explain it. But please, if you can't read it, explain where exactly you get stuck.

We begin at:

<x>=xx...xx for n+1 copies

And:

n, = <(>n+1<)<+n>>

That is:

0,=n+1=
1,=<(>1+1<)<+1>>=((2)+1+1)+1+1=6
2,=<(>3<)<+2>>=<(((3)+2+2+2)+2+2+2)+2+2+2=21
3,=<(>4<)<+3>>=(4)+3+3+3+3)+3+3+3+3)+3+3+3+3)+3+3+3+3=52

And so on.

n, = n^3+2n^2+2n+1

Next, when you find a 0 after a ,:

n,x0 = <(>n+1<),x>

0,0 = (0+1), = 1,=<(>1+1<)<+1>>=((2)+1+1)+1+1=6
1,0 = ((2),), = (21), = 10195

So, huh:

(1,0)/8

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 2:44 pm UTC

Okay, sounds good so far.

So, 2,0 would be (((3),),), equals ((52),), = (146121), ~ 3.12*10^15?

So, each number in the x,0 series seems to be about the cube of the last one, or about exponential growth.

Anyway I'll start on my own notation:

Define:
n[0] = 10^n
n$[m+1] = n$[m][m][m]...[m][m] with n [m]s
Where $ is anything.

Note that n[m] is equal to En##(m+1) in Extended Hyper-E Notation.

I submit 4[0]/7 ~ 1428.57
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 3:56 pm UTC

username5243 wrote:So, each number in the x,0 series seems to be about the cube of the last one, or about exponential growth.


Um, the cube of 6 is 216, while we get 10195 which is more than ^5ing.

10,0 = (((((((((((11),),),),),),),),),),),
=((((((((((1221),),),),),),),),),),
=(((((((((1823300986),),),),),),),),),
=((((((((6x10^27),),),),),),),),
=(((((((6x10^81),),),),),),),
=((((((6x10^243),),),),),),
=(((((6x10^729),),),),),
=((((6x10^2187),),),),
=(((6x10^6561),),),
=((6x10^19683),),
=(6x10^59049),
=6x10^177147

The equivalent of exponential growth would be:

(((((((((((11)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2)^2

=6x10^2132

Send:

(1,0)/7

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 4:00 pm UTC

Somewhere about x^x^x then.

Submit 3[0]*2 = 2000.
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 4:07 pm UTC

username5243 wrote:Somewhere about x^x^x then.


Yes, close to x^x^(x/2)

Submit:

(1,0)/5

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 4:08 pm UTC

3^7 = 2187
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 4:09 pm UTC

(1,0)/4

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 4:10 pm UTC

3*3[0] = 3000
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 4:12 pm UTC

(1,0)/3

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Re: My Number is Bigger! (again)

Postby username5243 » Sat Jun 27, 2015 4:14 pm UTC

Clearly we need to get bigger!

9001

OVER NINE THOUSAND!!!

Also the first number in the first "My Number is Bigger" thread.
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Re: My Number is Bigger! (again)

Postby Vytron » Sat Jun 27, 2015 7:17 pm UTC

1,0


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