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pages

## Unexpected edits

In your edit of User:Hyp cos/Catching Function Analysis p2, some "nowiki" tags disappeared, which caused many problems on the page. For instance, "Expansion depth limit exceeded" appeared and sections between "From $$C(\Omega^{\Omega+\omega})$$ to $$C(\Omega^{\Omega\omega})$$" and "From $$C(\Omega^{\Omega^\Omega}(\omega+1))$$ to $$C(\Omega^{\Omega^{\Omega2}})$$" disappeared. Fix them please, or undo your edits and leave the "\$ to MathJax" for me. {hyp/^,cos} (talk) 10:10, September 26, 2019 (UTC)

Oh I see. But please fix the problem quickly because I'm writing a page about R function vs "Normal" OCF vs Catching function and I need your page. 12AbBa (talk) 11:25, September 26, 2019 (UTC)

And have you read my page? Did you notice the similarity between EUAN and R function? 12AbBa (talk) 11:29, September 26, 2019 (UTC)

Thanks!!!! 12AbBa (talk) 10:01, September 30, 2019 (UTC)

Hello!

I'm the other kid interested in googology in your ohs homeroom class :)

Testitemqlstudop (talk) 13:20, October 21, 2019 (UTC)

Mango523WNR (talk) 10:09, February 9, 2020 (UTC)

Mr.12AbBa, I think I should see an ophthalmologist. Thank you Very much.

？？？？Zongshu Wu 15:53, February 9, 2020 (UTC)

Mango523WNR (talk) 00:04, February 10, 2020 (UTC)

## Extensions of BMS

> In this page, I will be analysing the most powerful recursive notation in the world (probably), BMS.

There are several non-naive extensions of BM2.3. If they are terminating and as strong as intended, then it is stronger than BMS.

p-adic 11:59, February 15, 2020 (UTC)

Hi. Could you tell me the precise definition of an OCF which you used in the analysis of BMS?

p-adic 14:47, February 19, 2020 (UTC)

AAAAAAAAARGH. the OCF issue. I know it will turn up sometime. Anyway, see my OCF page for the definition. Zongshu Wu 14:55, February 19, 2020 (UTC)

P.S. I always forget to sign and have to edit again :(

Also, Why are you asking about the OCF when I've barely started using it (only at the $$\psi(\omega)$$ level)? Zongshu Wu 15:17, February 19, 2020 (UTC)

Thank you for the clarification. So you are currently using the first OCF in your page on OCFs.
> Also, Why are you asking about the OCF when I've barely started using it (only at the $$\psi(\omega)$$ level)?
It is because
1. I strongly recommend googologists to clarify what OCF they are using in the analysis, because the traditional attitude to omit the clarification is one of the biggest reason why beginners will unintensionally mix-up distinct OCFs due to the lack of the knowledge of the existence of many OCFs. (This is related to this blog post on a proosal to use "specified" OCFs.)
2. I, as the one who verified the termination of pair sequence system, think that it is really hard to analyse pair sequences by standard OCFs in a precise manner, because the expansion of a complicated exression such as (0,0)(1,1)(2,2)(3,3)(2,2)(2,1) differs from the canonical system of fundamental sequences for standard OCFs. In particular, you are using an OCF including powers as a base function, and hence the difference looks pretty huge.
p-adic 22:44, February 19, 2020 (UTC)

> All OCFs are the same here.

Your analysis is wrong because the OCF in section 3 behaves in a different way.

> ψ(ψ_{I(1,0)}(0)) in section 4 and 5 = ψ(M) in section 6 and 7

Why isn't the right hand side ψ(ψ_{χ(M)}(0))?

p-adic 23:03, March 4, 2020 (UTC)

Could you explain this in more detail? Zongshu Wu 06:40, March 5, 2020 (UTC)

I mean, χ(χ(χ(χ(....)))) turns into an M, right? Zongshu Wu 06:49, March 5, 2020 (UTC)

I meant the following two:
1. The OCF in section 3 does not coincide with the OCFs in other sections up to ψ(ψ_{I(1,0)}(0)).
2. Since ψ_{χ(M)} in section 6 = ψ_{I(1,0)} in section 6, the correct equality should be "ψ(ψ_{I(1,0)}(0)) in section 4 and 5 = ψ(ψ_{χ(M)}(0)) in section 6 and 7" if I am correct.
The limit χ(χ(…)) coincides with ψ_{χ(M)}(0), and we have ψ(χ(χ(…))) = ψ(ψ_{χ(M)}(0)) << ψ(M). Or is there some restriction of the domain of χ? Since you have not defined the domains of your functions, I guessed that there are no restriction on the range of α.
p-adic 07:08, March 5, 2020 (UTC)

So what is $$\psi(M)$$ in your sense?Zongshu Wu 09:15, March 5, 2020 (UTC)

Do you mean the expansion? If there is no restriction on α as I guessed above, ψ(M) is simply expanded as ψ(χ(M_{M_{M_{…}}})), isn't it? If it is incorrect, please tell me the reason (and clarify the domain of χ, which is unspecified in the original definition). I note that since you have never defined an ordinal notation associated to your OCF, I am not certain whether we can define a decisive system of fundamental sequences. If you restrict α in ψ(α) to ordinals below χ(ε_{M+1}), then I guess that we have few problems arround it. However, since you are considering ψ(M), it can be problematic. I note that your OCFs are not similar to standard OCFs, and hence have many weird properties. (For example, consider the expansion of ψ(χ(ω)).)
p-adic 09:31, March 5, 2020 (UTC)

OK. So the thing is that when we are calculating ψ(M), χ(anything >M) is still undefined. So you can't just say that "ψ(M) is simply expanded as ψ(χ(M_{M_{M_{…}}}))".Zongshu Wu 10:00, March 5, 2020 (UTC)

Uh, right. Sorry, I just got confused with the condition γ<α. (I note that an OCF is not defined by a recursion in arithmetic, but is defined in transfinite induction in set theory. Therefore "it is strill undefined when it is defined" does not make sense. But OK, I understand what you wanted to say.) Since I am not good at calculating an OCF without an ordinal notation, I hope you to create it. Will you create an ordinal notation associated to your OCF?
p-adic 10:12, March 5, 2020 (UTC)

I do not know how to do that. Sorry. Or perhaps you could explain how to do that? Zongshu Wu 11:51, March 5, 2020 (UTC)

For example, I briefly explained how to do it here. Since creating an ordinal notation is the most important step in the study of computable googology using OCFs, it is significant if you create an ordinal notation associated to OCFs. (On the other hand, if you do not have an ordinal notation, it is extremely difficult for us and also you to precisely analyse your OCF, because the comparison can be uncomputable.)
p-adic 12:06, March 5, 2020 (UTC)

Can you give me an example of an ordinal notation associated to an OCF?Zongshu Wu 14:25, March 5, 2020 (UTC)

For example, the ordinal notation OT written in the article on Buchholz's function is the simplest one.
p-adic 14:27, March 5, 2020 (UTC)

😳! I can't understand! Zongshu Wu 14:32, March 5, 2020 (UTC)

Oops, OK. But I guess that you will understand soon :)
p-adic 14:36, March 5, 2020 (UTC)

can you and your friends help on my power of two wiki so you know i have asd cant do this by myself Fleetave1 (talk) 21:01, April 4, 2020 (UTC)

## Contact

Is there any way to contact you privately? I need to tell you something. 01:18, April 21, 2020 (UTC)

Oh, hi PsiCubed2. I have a skype account, however I don't know how you can reach me. Probably use the chat feature in some dead wiki, such as Username5243's https://allnumbers.fandom.com ?

Zongshu Wu 12:47, April 21, 2020 (UTC)

I went to that wiki and saw no chat feature. Oh well, I suppose it doesn't really matter. Plain'N'Simple (talk) 04:19, April 22, 2020 (UTC)

Fandom logged you out. Log back in. Zongshu Wu 12:34, April 22, 2020 (UTC)

I found it, but how is that private in any way? Anyone could join a chat, couldn't they?

At any rate, it really is no longer relevant. Plain'N'Simple (talk) 15:53, April 22, 2020 (UTC)

I do not consider Muhammad Bukhari noor (henceforth referred to as "Embi")'s extension of UNOCF to be an "official" part of UNOCF. Therefore, please do not add Embi's extensions to my user page on UNOCF, since I want only things I approve on that page. (Embi can keep doing it on his blog though - just don't mess with my page)

Thank you.

Username5243 (talk) 10:22, July 17, 2020 (UTC)

Then how about my extension instead? I wrote a definition in a way which you and other UNOCF users probably prefer.
p-adic 12:17, July 17, 2020 (UTC)

Sometime in mid-2020 I mentioned on the chat about an error in your Mahlo OCF, insisting it was ill-defined because $$\chi_{M_0}(0)$$ isn't a member of $$C(0,\beta)$$. I was wrong, and the OCF is indeeed well-defined, even though $$\chi_{M_0}(0)\not\in C(0,\beta)$$. I apologize for any inconvenience

It does have a property to watch out for called a "degenerate value" though, which happens because of this. Since $$\Omega=\chi_{M_0}(0)\not\in C(0,\beta)$$, then $$\psi_{\Omega_2}(0)=\varepsilon_0$$. Then $$\Omega=\chi_{M_0}(0)\in C(1,\beta)$$, so $$\psi_{\Omega_2}(1)=\varepsilon_{\Omega+1}$$, $$\psi_{\Omega_2}(2)=\varepsilon_{\Omega+2}$$, etc. and as usual C7X (talk) 03:09, 17 February 2021 (UTC)

## Set-builder notation

On your site, something quite interesting is mentioned. I've never heard that {x:...} represents a class, while {x|...} represents a set. MathOverflow said they both mean the same thing, but which convention should I use? C7X (talk) 23:13, 10 March 2021 (UTC)

Right, {x:...} is the same as {x|...}.
p-adic 23:16, 10 March 2021 (UTC)

Anyways that chapter is super WIP and has a bajillion mistakes probably. And BTW how do you even write a class? Zongshu Wu 06:45, 11 March 2021 (UTC)

You can write a class in the same way as a set. Say, {x|¬(x∈x)} is a class. (A set is a special sort of a class, and hence you do not have to distinguish them unless you are working in what is called 2-sorted theory.)
p-adic 08:31, 11 March 2021 (UTC)

## Constructible Hierarchy

If you're still interested in learning about how the constructible hierarchy works (as you said here). Unfortunately these are complicated concepts that beginners will have to study a lot to understand in full (I'm not an expert and not done studying either).

Here are some nice papers to look through (although all of these contain things I don't know):

• [1] This is probably one of my favorite papers of all time. The only drawback here is its lack of sources for some statements
• [2], I don't know some things recommended to learn here such as "proof that L models ZFC+GCH+V=L", but even the introduction alone is nice in terms of an explanation of how the stages Lα are defined. Later in this paper there are also some theorems about things such as projecta ("Σn-hard-cores"), nonprojectible ordinals, and others as well
• [3] This paper is a bit more advanced, and since it's an old paper some notation is different than what's used today (for example, using "$$\omega_1$$" instead of $$\omega_1^{CK}$$ to denote the Church-Kleene ordinal)
• I've also tried to clean up the Constructible universe page on this wiki to appear clearer.

Also, please try not to make the mistake that I made where I tried to "learn" large ordinals by looking at tables of analysis (PBot explained here why looking at analyses isn't the same as learning a concept) C7X (talk) 01:48, 29 March 2021 (UTC)

Thanks so much! I also used to learn ordinals by looking at analysis, but I don't do that anymore :) Zongshu Wu 11:30, 29 March 2021 (UTC)

## Licensing information

p-adic 09:26, 16 June 2021 (UTC)

It's a Saibian creation and can be found on one of his pages. I do not know how to add licensing info, can you please do so for me? Zongshu Wu 03:10, 22 June 2021 (UTC)

In that case, you are perhaps uplaoding Saibian's copyrighted image without permission. Since it is not allowed in FANDOM, I ask admins to delete it as a request from you.
p-adic 04:41, 22 June 2021 (UTC)

## global.js and global.css

What is the purpose of creating these pages actually? ARsygo (talk) 01:45, 19 August 2021 (UTC)

I shouldn't have created these pages on GWiki. If you copy paste