BUMP

Is my analysis of ah correct?

If not, how powerful is @@@ actually?

## Search found 2701 matches

- Today, 12:47 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

- Today, 7:45 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

sup{e_w,e_w^w,e_w^w^w, etc.}testitemqlstudop wrote: ↑Yesterday, 11:19 pmHow is e_e0 defined? "e0-th fixed point of a |-> w^a" doesn't make sense as the "fixed point" stuff only work for integers

- Yesterday, 11:49 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Rules with interesting dy/dx

Just want to see if anyone thinks that there's a copy of the thread in question here

- Yesterday, 11:25 am
- Forum: The Sandbox
- Topic: Talk to Transformer
- Replies:
**135** - Views:
**15697**

### Re: Talk to Transformer

In order to make the Formal logic make sense it's best to prefix stuff with the following or similar ∀x(x=x) ∀x∀y(x=y⇒y=x) ∀x∀y∀z(x=y&y=z⇒x=z) ∀x∃y(y>x) It makes stuff like this: Recently the mathematician Jheyeorggkht Anter determined that the transfinite ordinal w satisfies the condition ∃x(w>x) ,...

- Yesterday, 11:10 am
- Forum: The Sandbox
- Topic: Talk to Transformer
- Replies:
**135** - Views:
**15697**

### Re: Talk to Transformer

Recently a mathematician (the late etal eht) determined that ∃y∀x∈N(y>x⇒x∉y). He then worked out an equation for the sum of a set of primes: (y)y∈{(y)}. So for some positive number (∞, ∞), x⇒x∉y, and y≠x, there is a function y∈{x, y}∈N(x⇒y). This is called the sum of powers. Theorem: (y)∈{x, y}. Th...

- Yesterday, 10:53 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

And now, a block of text where I repeatedly choose the first suggestion from the Mac autocomplete: of the day and the end of the day I guess you can do it and then I’ll be sure to ask you if you have any questions or not how you can get the money to the end of the year and the end of the year and t...

- Yesterday, 10:51 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

I made a testing discord server for fun

- Yesterday, 9:40 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

### Re: Ordinals in googology

I'm gonna try to figure out how much more powerful ah_n{a[[1]]a} is than f_a(n) ah_n {a@n} > f_an(n) which is around f_aw(n) ah_n {a@a@n} > (assuming reasonable ah rule extensions) ah_n {a@an} > f_((a^2)*n)(n) ah_n {a//w} = ah_n {a//n} probably > f_a^w(n) (probably even without the reasonable extens...

- Yesterday, 9:19 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

- Yesterday, 8:28 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

Rule of thumb: with large limit ordinals, taking [1] is acceptable, and [2] is not. For instance: Rule: keep taking [1] gamma_0 phi_w(0) e_0 1 Rule: keep taking [2] gamma_0 phi_phi_w(0)(0) phi_z_0(0)(0) phi_e_e_0(0) I will show you the expansion of e_e_0: e_w e_2 w^w^(e_1 +1) w^(e_1*2) (I think this...

- November 16th, 2019, 10:15 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

### Re: Ordinals in googology

That wasn't the question-- the question is whether that's the limit of Madore's psi Then BHO is the supremum of Madore's psi, and what the heck is ψ(Ω_ω) But it says that ψ1(0) = ε_Ω+1 (which is uncountable), not ψ(ε_Ω+1). Is that a mistake? No Then I don't understand. The BHO = ψ(ψ_1(0))

- November 16th, 2019, 10:06 am
- Forum: Other Cellular Automata
- Topic: MaritimeLife (B2i34c6cen7c8/S2-i3-q4c5a6e8)
- Replies:
**6** - Views:
**349**

### Re: MaritimeLife (B2i34c6cen7c8/S2-i3-q4c5a6e8)

Bump Are there any ways to make the junk here or something similar? x = 21, y = 20, rule = B2i34c6cen7c8/S2-i3-q4c5a6e8 13bo$13b3o2$17bo$11bo4b5o$10bob2o2bo3bo$12b2o3bobo$13bo4bo$12bo$11b2o 2$19bo$18b3o2$18bobo$18b3o2$3o$2bo$bo! Or maybe this junk? x = 16, y = 16, rule = B2i34c6cen7c8/S2-i3-q4c5a6e8...

- November 16th, 2019, 9:48 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

Question:

How do you make codeblocks on the discord server?

How do you make codeblocks on the discord server?

- November 16th, 2019, 9:25 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

### Re: Ordinals in googology

I searched one more source http://quibb.blogspot.com/2012/03/infinity-extended-collapsing-functions.html and it also says the BHO is ψ(Ω^Ω^Ω^Ω^...) = ψ(ε_Ω+1). That wasn't the question-- the question is whether that's the limit of Madore's psi But it says that ψ1(0) = ε_Ω+1 (which is uncountable), ...

- November 16th, 2019, 9:15 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

How to make arbitrary constants:

1) think of a series that converges, e.g. ∑(x=2 to oo) (Tan((pi(x^sin(pix/(2x-2))-1)/(2x)))/(x^3))

2) input into wolfram alpha

1) think of a series that converges, e.g. ∑(x=2 to oo) (Tan((pi(x^sin(pix/(2x-2))-1)/(2x)))/(x^3))

2) input into wolfram alpha

Code: Select all

`0.14844504016840183957974730421752299599269733510964683413522844065772496144761544195904135014573913904080552414421533`

- November 16th, 2019, 8:29 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

### Re: Ordinals in googology

Slight update to @@@ I'll put the whole definition of ah up to @@@ in this code: Part one: define $_n as any entries (including no entries) in an array. It’s my symbol for we-don’t-care entries. In any one use of any one rule, if n is the same, $_n is the same a#b = concatenation of a and b n@m = n,...

- November 16th, 2019, 7:44 am
- Forum: The Sandbox
- Topic: Largest total computable function competition
- Replies:
**152** - Views:
**15044**

### Re: Largest total computable function competition

What would happen if you defined TREEEE(n) similarly to TREE(n) but you allowed Aidan-mode-esque nesting of parentheses? Note: homeomorphic embeddability-wise, it would be two nodes each connected to each other, neither as a parent or a child-- {([)]} would be a triangle where each node was connecte...

- November 16th, 2019, 7:30 am
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

There are aleph-naught types of people in this world Those who stopped after reading this [line] Those who stopped after reading this Those who stopped after reading this Those who stopped after reading this Those who stopped after reading this Those who stopped after reading this Those who stopped ...

- November 16th, 2019, 7:17 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**138** - Views:
**2433**

### Re: Ordinals in googology

Oh, whoops. The Bachmann-Howard ordinal is not in madore's psi but in weirmann's theta. Sorry. Yeah, psi(w_w) > psi(e_(W+1)) The Wikipedia artivle about OCF's says that the Bachmann-Howard ordinal is the supremum of psi(W), psi(W^W), psi(W^W^W), psi(W^W^W^W)... and we can't go any further with the ...

- November 15th, 2019, 9:07 pm
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: Random posts

There are 100 types of people in this world Those who think that's a lot Those who think that's too few Those who think this is in binary Those who know this isn't in base-10 Those who just realized this wasn't in binary Those who think that this isn't in base g64 Those who have fit into more than o...

- November 15th, 2019, 8:53 pm
- Forum: The Sandbox
- Topic: Game Of Life Comics
- Replies:
**56** - Views:
**18309**

- November 15th, 2019, 8:19 pm
- Forum: The Sandbox
- Topic: Random posts
- Replies:
**3303** - Views:
**398864**

### Re: EvinZL's first time doing googology functions

The title is misleading; I did it a few times before but they are too pathetic to mention. :shock: This one isn't. define :shock: (n, m, l, d) as follows: :shock: (n, m, l, 1) = m^^^^...^^^m with n up-arrows. :shock: (n, m, l, d) = :shock: (n, m, :shock: (n, m, l - 1, d), d - 1) :shock: (n, m, 0, d...

- November 15th, 2019, 8:02 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**303** - Views:
**72748**

### Re: Thread for Non-CA Academic Questions

Are there any online SKIO calculus websites? I've already seen a SKI calculus one.

- November 15th, 2019, 7:23 pm
- Forum: Other Cellular Automata
- Topic: Miscellaneous Discoveries in Other Cellular Automata
- Replies:
**1471** - Views:
**293915**

### Re: Miscellaneous Discoveries in Other Cellular Automata

Cartainly known gun in wlife: x = 26, y = 39, rule = B34w/S23 19bo$17b3o$16bo$16b2o$5b2o15b2o$6bo15bo$6bobo11bobo$7b2o11b2o3$24b2o$ 24bo$22bobo$22b2o$14bo$13b2o$14bo$2o3b2o$obobobo$2bobo$b2obobo$5b2o$ 14bo$13b2o$14bo7$7b2o11b2o$6bobo11bobo$6bo15bo$5b2o15b2o$16b2o$16bo$ 17b3o$19bo! It looks like abhp...

- November 15th, 2019, 6:25 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**303** - Views:
**72748**

### Re: Thread for Non-CA Academic Questions

Hold it wait, I just joined. To confirm, I am Moooosey#7155.fluffykitty wrote: ↑November 14th, 2019, 6:28 pmStill not sure why you haven't joined the Googology Discord yet btw