Search found 1232 matches

by testitemqlstudop
Yesterday, 11:19 pm
Forum: The Sandbox
Topic: Random posts
Replies: 3303
Views: 398556

Re: Random posts

How 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
by testitemqlstudop
November 14th, 2019, 8:18 pm
Forum: The Sandbox
Topic: Largest total computable function competition
Replies: 152
Views: 15038

Re: Largest total computable function competition

Moosey wrote:
November 14th, 2019, 9:35 am
I think that's still has a problem. You're making W(1,1) = W(W(1,1),0) = W(W(1,1)), right? You can't use the same array because otherwise you have issues like this.
What? W takes an array and returns an integer.
W([1, 1]) = W([W([1, 0]), 0]) + 1.
by testitemqlstudop
November 14th, 2019, 9:21 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

Let S_i be a set theory. S_0 = ZFC, and S_i is the axiom set that can prove S_{i-1} well-founded. Assume that S_i will always be provably well founded, since otherwise ZFC isn't a well founded set theory. My function is the Rayo-analogue function. but instead of FOST we have S_{10^100}. Has got to ...
by testitemqlstudop
November 14th, 2019, 2:05 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

Let S_i be a set theory. S_0 = ZFC, and S_i is the axiom set that can prove S_{i-1} well-founded. Assume that S_i will always be provably well founded, since otherwise ZFC isn't a well founded set theory. My function is the Rayo-analogue function. but instead of FOST we have S_{10^100}. Has got to b...
by testitemqlstudop
November 12th, 2019, 9:16 am
Forum: Website Discussion
Topic: Like button in forum request
Replies: 33
Views: 10456

Re: Like button in forum request

Aha. Doesn't that automatically prove a dislike button should exist? Otherwise why would they use it?
by testitemqlstudop
November 11th, 2019, 10:13 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

Since my last attempt at a FPT was trash, I made another:

https://googology.wikia.org/wiki/User_b ... udop/FPT_2
by testitemqlstudop
November 11th, 2019, 10:11 pm
Forum: Website Discussion
Topic: Like button in forum request
Replies: 33
Views: 10456

Re: Like button in forum request

I disagree with Goldberg, who disagrees with Calyman, who is agreed by me; hence, Calcyman disagrees with Goldberg.
by testitemqlstudop
November 7th, 2019, 2:19 am
Forum: Scripts
Topic: Geneascopy
Replies: 6
Views: 2387

Re: Geneascopy

Oh wow you're back? So far, the only rule to show similar behaviour to CGoL is B37e/S23, which, beyond the collective [linear growths]*P(linear growths) after gen 5470, shows a similar dip followed by a rapid increase with loads of fine structure, although obviously reaching higher populations. A le...
by testitemqlstudop
November 6th, 2019, 10:07 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

Ascending TMs Consider a "Universe ascend" which can reach another Universe of dimensions. You can't. There isn't a next universe, we have already took up all the space... ...unless you index dimensions by ordinals, and invent some method of fixed-point leap. i.e. we originally had 1d, 2d, ... nd, ...
by testitemqlstudop
November 5th, 2019, 8:54 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

OMG I KNOW I believe the fastest growing known computable functions are of the following form: n ↦ The combined running time of all Turing machines (with no input) such that there exists a proof that they halt in second-order PA using fewer than n symbols FIrst order set theory is much stronger, and...
by testitemqlstudop
November 4th, 2019, 11:30 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

Is the well ordering of w_1 provable? Isn't well-orderedness part of the definition of an ordinal? If I'm missing something, then see this proof (set X to be the set of natural numbers to get the conclusion that ω_1 exists and is well-ordered) Several things: The well ordering of w_1 implies the we...
by testitemqlstudop
November 3rd, 2019, 12:29 am
Forum: The Sandbox
Topic: Random posts
Replies: 3303
Views: 398556

Re: Random posts

JP21 wrote:
November 2nd, 2019, 11:21 am

Yeah but not everyone speaks chinese and english is the most universal language.
Ab, V fcrnx ebg13
by testitemqlstudop
November 2nd, 2019, 11:48 pm
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

No it doesn't solve its own halting problem. It executes on a higher level as soon as it ascends; it can't descend. Hence, it can never solve its own halting problem, since to solve the halting problem on its current level it needs to ascend to the next level.
by testitemqlstudop
November 2nd, 2019, 11:47 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

Is the well ordering of w_1 provable?
by testitemqlstudop
November 2nd, 2019, 4:14 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

Consider a Turing machine with another added state, "ascend", which makes a new tape called the "ascended tape" and all previous tapes are called "lower tapes". The head is allowed to read/write to the ascended tape and the lower tapes, and the ascended tape has the ability to solve the Halting pro...
by testitemqlstudop
November 2nd, 2019, 4:08 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 24
Views: 1489

Re: Largest total uncomputable function competition

Consider a Turing machine with another added state, "ascend", which makes a new tape called the "ascended tape" and all previous tapes are called "lower tapes". The head is allowed to read/write to the ascended tape and the lower tapes, and the ascended tape has the ability to solve the Halting prob...
by testitemqlstudop
November 2nd, 2019, 3:11 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

Moosey wrote:
November 1st, 2019, 5:35 pm
The binary Veblen phi function.
gameoflifemaniac wrote:
November 1st, 2019, 5:17 pm
Also, what is the largest countable ordinal?
There is no such thing. If you say that a is the largest countable ordinal, then I can point out that a+1 is larger.
sup{a<w_1^CK:a}
by testitemqlstudop
October 31st, 2019, 11:14 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

Isnt T0 the result of the diagonalization of e0, z0, n0, etc? i.e. e0 = w^^2 [sic], z0 = w^^^2, n0 = w^^^^2 I remember you said somewhere T0 = w^^w, obviously that's a large underestimation T0? Do you mean gamma_0? gamma_0 is certainly not the supremum (which is what you mean-- I won't argue with P...
by testitemqlstudop
October 31st, 2019, 8:44 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

e0 is the first solution to a = w^a, or a transfinite power stack of w's. Adding another w will not change the number.
by testitemqlstudop
October 31st, 2019, 9:13 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

I have defined an OCF, a fat version of it, and an accompanying fundamental sequence system. ... See my blog post here: https://testitem.github.io/colg/fpt.html That's not a traditional OCF-- OCFs are defined differently, like this: C_0(x) = set C_n+1(x) = C_n(x) U {operations with a and b in C_n(x...
by testitemqlstudop
October 31st, 2019, 2:27 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

I have defined an OCF, a fat version of it, and an accompanying fundamental sequence system. I have took the limit of the fat OCF function and defined the fundamental sequence for it as well. (Note that the fat OCF system isn't exactly "more powerful", but instead "simpler".) You can see where this ...
by testitemqlstudop
October 25th, 2019, 11:16 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

What is the cardinality of the set of: 1) all ordinals; 2) all countable ordinals; 3) all computable ordinals. 3) ℵ_0 That does not make sense; you can infinitely exponentiate w and add them together (this is further enlargened by the branching possibilities of each exponent and coefficient), so un...
by testitemqlstudop
October 25th, 2019, 7:34 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

My argument for Latex is with such a complicated definition, with no formatting it's difficult to understand.

What is the cardinality of the set of:

1) all ordinals;
2) all countable ordinals;
3) all computable ordinals.

1 is at least beth_2.
by testitemqlstudop
October 24th, 2019, 8:45 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 137
Views: 2424

Re: Ordinals in googology

PLEASE USE LATEX

And to say something constructive I'm going to use p-adic's fundamental sequence argument
8a. ah_n((0@a)#{b,$_6}) = ah_n((0@(a[n])#{b,$_6}), a a lim ord
That does not work with your recursive definition at all.