Search found 815 matches

by gameoflifemaniac
November 16th, 2019, 10:30 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

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) No Then I don't understand. The BHO = ψ(ψ_1(0)) Now everything has become clear for me Or is it? Madore's psi C(a) set includes ordinals in the f...
by gameoflifemaniac
November 16th, 2019, 10:11 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

Moosey wrote:
November 16th, 2019, 9:25 am
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)
Moosey wrote:
November 16th, 2019, 9:25 am
gameoflifemaniac wrote:
November 16th, 2019, 9:19 am
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.
by gameoflifemaniac
November 16th, 2019, 9:19 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I searched one more source http://quibb.blogspot.com/2012/03/infin ... tions.html
and it also says the BHO is ψ(Ω^Ω^Ω^Ω^...) = ψ(ε_Ω+1).
But it says that ψ1(0) = ε_Ω+1 (which is uncountable), not ψ(ε_Ω+1). Is that a mistake?
by gameoflifemaniac
November 16th, 2019, 8:02 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I'll post the guide once more for everybody who knows nothing about googology. ωεζηφαψΓ 0,1,2,3,4,5,6... ω ω, ω+1, ω+2, ω+3, ω+4,... ω+ω = ω2 ω, ω2, ω3, ω4, ω5,... ω*ω = ω^2 ω^2, ω^3, ω^4, ω^5,... ω^ω ω, ω^ω, ω^ω^ω, ω^ω^ω^ω,... ω^ω^ω^ω^ω^ω^ω^... = ε_0 0th fixed point of α = ω^α ε_0+1, ω^(ε_0+1), ω^ω...
by gameoflifemaniac
November 16th, 2019, 6:09 am
Forum: The Sandbox
Topic: Random posts
Replies: 3302
Views: 398265

Re: Random posts

There are 2 types of people in the world. Whose who always end a sentence and those
by gameoflifemaniac
November 16th, 2019, 3:56 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

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 ...
by gameoflifemaniac
November 15th, 2019, 4:24 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I literally wrote that since the limit of Madore's psi is the Bachmann-Howard ordinal, psi(w_w) is no larger than the Bachmann-Howard ordinal. With Madore's psi, a>b does not mean that psi(a) > psi(b). It just means psi(a) >= psi(b). So in other words, psi(w_w) = the Bachmann-Howard ordinal. So why...
by gameoflifemaniac
November 15th, 2019, 3:32 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I meant f_w_1CK(n) in the fast-growing hierarchy. Yes, I said it would make sense if you have a fundamental sequence for w_1ck and then explained a possibility What is ψ(Ω_ω)? I asked this before Depends on which of a gazillon ordinal collapsing functions you're using-- if it's madore's psi, it's t...
by gameoflifemaniac
November 15th, 2019, 10:46 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

Can the Bachmann-Howard ordinal be explained in terms of a simpler notation? What is ψ(Ω_ω)? I asked this before
by gameoflifemaniac
November 15th, 2019, 10:43 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I had 2 more questions in the previous post. Does the function f_w_1CK(n) make any sense? Yes, theoretically. But only if you have a fundamental sequence for w_1CK--which is still possible. E.g. w_1ck[n] = min a > all ordinals definable in n symbols in some language like set theory, or something e....
by gameoflifemaniac
November 13th, 2019, 4:49 pm
Forum: The Sandbox
Topic: Random posts
Replies: 3302
Views: 398265

Creeper: Aww man

Creeper Aw man So we back in the mine Got our pickaxe swinging from side to side Side-side to side This task, a grueling one Hope to find some diamonds tonight, night, night Diamonds tonight Heads up You hear a sound, turn around and look up Total shock fills your body Oh, no, it's you again I can n...
by gameoflifemaniac
November 13th, 2019, 4:38 pm
Forum: The Sandbox
Topic: Make the most ridiculous SI derived unit!
Replies: 9
Views: 384

Re: Make the most ridiculous SI derived unit!

How do you construct the coulomb out of simpler units?
by gameoflifemaniac
November 13th, 2019, 4:36 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I had 2 more questions in the previous post.
Does the function f_w_1CK(n) make any sense?
by gameoflifemaniac
November 13th, 2019, 3:53 pm
Forum: The Sandbox
Topic: Introductions
Replies: 83
Views: 57217

Re: Introductions

But it's not very natural.
by gameoflifemaniac
November 13th, 2019, 12:48 pm
Forum: The Sandbox
Topic: Introductions
Replies: 83
Views: 57217

Re: Introductions

Have been here for a while, but didn't introduce myself. My name is Franek. I'm 13 years old and I live in Poland. I was interested in mathematics and science since I can remember. Conway's Game of Life has been my hobby for 3 years. Now I'm actually less into science and more into memes and video g...
by gameoflifemaniac
November 13th, 2019, 12:36 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

Can the Bachmann-Howard ordinal be explained in terms of a simpler notation? What is ψ(Ω_ω)? BHO is the supremum of Madore's psi, so how can this be any bigger?
by gameoflifemaniac
November 13th, 2019, 11:01 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

PHPBB12345 wrote:
November 13th, 2019, 6:00 am
How small is reciprocal of transcendental integer?
What the

Also, if W is w_1, what is W_1?
by gameoflifemaniac
November 13th, 2019, 11:00 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

I've got a complete guide to ordinal numbers up to LVO. For those who know nothing about them. ωεζηφα Γ 0,1,2,3,4,5,6... ω ω, ω+1, ω+2, ω+3, ω+4,... ω+ω = ω2 ω, ω2, ω3, ω4, ω5,... ω*ω = ω^2 ω^2, ω^3, ω^4, ω^5,... ω^ω ω, ω^ω, ω^ω^ω, ω^ω^ω^ω,... ω^ω^ω^ω^ω^ω^ω^... = ε_0 ε_0+1, ω^(ε_0+1), ω^ω^(ε_0+1), ...
by gameoflifemaniac
November 12th, 2019, 5:13 pm
Forum: The Sandbox
Topic: Random posts
Replies: 3302
Views: 398265

Re: Random posts

Moosey wrote:
November 12th, 2019, 3:35 pm
gameoflifemaniac wrote:
November 12th, 2019, 1:46 pm
This is the one-and-only fatest growing function

y = 1/(1-x)
But it's eventually dominated by y=x
bruh
by gameoflifemaniac
November 12th, 2019, 5:02 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

SVO is the fixed point of what? I've got a complete guide to ordinal numbers up to LVO. For those who know nothing about them. ωεζηφα Γ 0,1,2,3,4,5,6... ω ω, ω+1, ω+2, ω+3, ω+4,... ω+ω = ω2 ω, ω2, ω3, ω4, ω5,... ω*ω = ω^2 ω^2, ω^3, ω^4, ω^5,... ω^ω ω, ω^ω, ω^ω^ω, ω^ω^ω^ω,... ω^ω^ω^ω^ω^ω^ω^... = ε_0 ...
by gameoflifemaniac
November 12th, 2019, 1:46 pm
Forum: The Sandbox
Topic: Random posts
Replies: 3302
Views: 398265

Re: Random posts

This is the one-and-only fatest growing function

y = 1/(1-x)
by gameoflifemaniac
November 9th, 2019, 4:09 am
Forum: The Sandbox
Topic: Random posts
Replies: 3302
Views: 398265

Re: Random posts

lol
by gameoflifemaniac
November 9th, 2019, 3:33 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

Wow.

What is the Bachmann-Howard ordinal?
by gameoflifemaniac
November 8th, 2019, 3:57 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

gameoflifemaniac wrote:
November 8th, 2019, 11:42 am
What is phi(1,1,0), phi(2,0,0)?
And is the Ackermann ordinal equal to Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ...?
This
Also, I can't appreciate your ah function cuz small brain
by gameoflifemaniac
November 8th, 2019, 11:42 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2423

Re: Ordinals in googology

What is the large Veblen ordinal? I know it's defined by α↦φ_Ω^α(0), but can you even talk about phi of an uncountable cardinal?
What is phi(1,1,0), phi(2,0,0)?
And is the Ackermann ordinal equal to Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ_Γ...?