User talk:LittlePeng9

Welcome
Hi, welcome to ! Thanks for your edit to the Talk:Subcubic graph number page.

Please leave a message on my talk page if I can help with anything! -- Ikosarakt1 (Talk) 16:18, January 28, 2013

wikiballs
try this out. $Jiawhein$\(a\)\(l\)\(t\) 09:28, March 16, 2013 (UTC)

Transfinite
Note: omega and Epsilon-zero is not infinite. $Jiawhein$\(a\)\(l\)\(t\) 11:48, March 29, 2013 (UTC)


 * Depends on how one defines infinite. If we mean with it that something is larger than anything finite then transfinite -> infinite. LittlePeng9 (talk) 12:03, March 29, 2013 (UTC)

Template:wedges
Vote now! $Jiawhein$\(a\)\(l\)\(t\) 12:11, April 26, 2013 (UTC)

Congrats
Congrats you with birthday and age \(2 \uparrow\uparrow 3\). Ikosarakt1 (talk ^ contribs) 11:47, May 23, 2013 (UTC)

Actually, today I hit 15. I earlier said I'm 15 because of rounding error. So yeah, smallest odd semiprime. LittlePeng9 (talk) 13:43, May 23, 2013 (UTC)

By the way, soon I shall reach really important milestone: July 8, 2013 I shall live my half-billionth second. Ikosarakt1 (talk ^ contribs) 14:20, May 23, 2013 (UTC)

Congratulations with your birthday (and age \(2 \downarrow\downarrow 3\), this time for real :P) Wythagoras (talk) 18:54, May 23, 2014 (UTC)

Please, stop undo edits
Please, stop undo Ikosarakts edits. It is easy to fix. Wythagoras (talk) 09:13, August 8, 2013 (UTC)

Sorry, didn't know you edit them too. LittlePeng9 (talk) 09:18, August 8, 2013 (UTC)

Temporarily I got a laptop just now, so I can edit normally. Ikosarakt1 (talk ^ contribs) 11:45, August 8, 2013 (UTC)

Hey, so you're an admin now, considering that I won't be around much and Ikosarakt could use some support. FB100Z &bull; talk &bull; contribs 20:42, September 22, 2013 (UTC)

name
i kinda...found out your real name while stumbling upon a publicly available source. i won't disclose anything publicly to avoid drawing attention to it, but next time on chat i'll PM you where i found it so you can cover up. sorry :/ you're.so.pretty! 08:54, April 12, 2014 (UTC)


 * You don't have to be sorry, I expected you to find it eventually :P I wouldn't touch that topic if I wasn't aware of possible consequences. I don't consider my name to be any sort of top secret, if you asked me I'd tell you. But still I'm quite curious about where you have found it. LittlePeng9 (talk) 11:18, April 12, 2014 (UTC)


 * Woah actually that was very easy to find haha King2218 (talk) 13:29, April 12, 2014 (UTC)

prime counting function in FOA
so i have all the pieces in place for defining \(\pi(n)\), except one that seems potentially problematic, namely a function that counts the number of 1's in the binary expansion of n. any ideas? you're.so.pretty! 22:15, April 14, 2014 (UTC)
 * okay so OEIS tells me that this function is also equivalent to the largest integer a such that \(2^a | \binom{2n}{n}\), or \(2^a | \frac{(2n)!}{n!^2}\), but i don't see how to do factorials. every step i take seems to do some sort of goalpost moving you're.so.pretty! 00:51, April 15, 2014 (UTC)


 * I think I have found everything we need: here (pages 294-298) are preliminary definitions for defining exponentiation, but I'm pretty sure this can be used to define sequence of primes, and thus also \(\pi(n)\). Idea is to have a number which codes all numbers up to a given point, and from this it is possible to add next number to this sequence. This will work, but won't be easy to formalize. LittlePeng9 (talk) 10:51, April 18, 2014 (UTC)
 * looks like Hájek and Pudlák managed to write the Hamming weight function. at least we know it's possible now you're.so.pretty! 17:29, April 18, 2014 (UTC)

check it
bam you're.so.pretty! 22:57, May 23, 2014 (UTC)

bam LittlePeng9 (talk) 04:20, May 24, 2014 (UTC)

surreal fundseqs
i realize now that if we allow non-monotonic fundseqs, we can do something like w/2 = lim(0, w, 1, w-1, 2, w-2, ...). however i'm not aware of any definitions of the limit for surreal numbers, so maybe i'm rejoicing too soon you're.so.pretty! 20:59, June 10, 2014 (UTC)


 * I don't think there is any useful notion of limit in surreal numbers world, because, for example, between two "walls" of this limit there still is w/2+1, w/2-1, not to mention the whole wilderness of sums of infinitesimals. I, however, don't rule out existence of limits in surreals, though I can't even see when we can call sequence convergent. LittlePeng9 (talk) 21:22, June 10, 2014 (UTC)
 * w/2+1 and w/2-1 seem like they would fall on the other side of a classification of surreals analogous to limit vs. successor ordinals. Although I've unfortunately misplaced my copy of ONAG (it'll turn up sooner or later), I wouldn't be surprised if Conway has already discovered and formalized that distinction. Maybe it's something like having a limit ordinal birthday, I'm not sure. you're.so.pretty! 23:11, June 10, 2014 (UTC)


 * I think of the following definition for non-monotonic sequence a_1,a_2,... It's a number a with the least birthday value, and, for every natural number n, there are k,l>n such that a_k, having order type at most w 3) all elements in L are strictly less than all those in R. Then lim2(S) = {L|R}. lim2 is not total (at least not over the power set of On2) but I think it is single-valued &mdash; that is, it seems that the L/R partition is unique. you're.so.pretty! 07:32, June 11, 2014 (UTC)

Proof of uniqueness: Let L1/R1 and L2/R2 be two such partitions of S. We wish to show that L1 = L2.

If L1 and L2 are both empty, then we are done. Otherwise, let x be the least element of L1, which exists because L1 is well-ordered by <. x must therefore be the least element of S (any smaller elements must belong to R1, which contradicts condition 3). Now x belongs to either L2 or R2. Suppose x belongs to R2: L2 is empty and x is the least element of R2. But since S is infinite, so is R2, and therefore its order type with respect to < is at least w. Since R2 has a least element, its order type cannot be w, which contradicts condition 2. Therefore, x is in L2.

Since x is in both L1 and L2, we consider S \ {x} as partitioned by (L1 \ {x})/R1 and (L2 \ {x})/R2. We can make the same argument by induction.

you're.so.pretty! 17:57, June 11, 2014 (UTC)


 * Note: induction will work here because, by assumption, L1 and L2are both well-ordered. LittlePeng9 (talk) 18:10, June 11, 2014 (UTC)

Continued fractions: Copeland-Erdos vs. Champernowne
Here's why the Champernowne constant has such a spiky continued fraction and Copeland-Erdos does not. Far into the digits of the former, you get very close to periodic behavior:


 * ...184732861184732862184732863184732864184732865184732866...

which is a few digits off a perfectly repeating decimal. This means that the Champernowne constant will be extremely close to certain rational numbers. We have to take a bit of leap of faith to assume that some of these will be its convergents, but if this link is legitimate, it explains the spikes very well. An unusually close convergent needs to be compensated for with a large term in the continued fraction.

The lack of spikes in the Copeland-Erdos constant is a consequence of prime gaps getting wider and wider as we approach infinity, so there's less room for the periodicity as seen in Champernowne. However, spikes DO happen. They're just rarer than that of the Champernowne constant since the primes grow faster.

I would like to try a simulation to test the theory that concatenation of slower-growing integer sequences results in spikier continued fractions. you're.so.pretty! 21:20, July 30, 2014 (UTC)


 * Thanks for that explanation. I actually had an idea on why this is so. I wonder if Champernowne's constant is Liouville. Such enormous terms in continued fraction strongly suggest so, but I wasn't able to find any mention of that fact. LittlePeng9 (talk) 21:30, July 30, 2014 (UTC)


 * interestingly, Champerowne's constant has an irrationality measure of 10. Deedlit11 (talk) 22:54, July 30, 2014 (UTC)
 * What happens if we change the base? you're.so.pretty! 23:51, July 30, 2014 (UTC)
 * The base-b Champerowne's constant has an irrationality measure of b. Deedlit11 (talk) 02:30, July 31, 2014 (UTC)

TM specialist
Yes, I think I would agree with that. Wythagoras (talk) 12:02, August 3, 2014 (UTC)


 * I'm a TM specialist too:


 * 0 * 1 r 0


 * King2218 (talk) 13:12, August 3, 2014 (UTC)
 * Neat! Yes, you are certainly a TM specialist. Maybe you'll get a Fields Medal for this discovery! Wythagoras (talk) 14:08, August 3, 2014 (UTC)
 * dude this is a new chapter in TM research. i cant believe it man, thats brilliant you're.so.pretty! 19:56, August 3, 2014 (UTC)
 * You wouldn't believe it guys, but this machine can solve the halting problem! :) King2218 (talk) 14:19, August 4, 2014 (UTC)
 * Oh my god, yes, you are 100% right - I wouldn't believe it :) LittlePeng9 (talk) 14:54, August 4, 2014 (UTC)
 * I hope I get this right. Is is that if it runs longer than this machine it doesn't halt and if it runs less steps it halts or so? :P Wythagoras (talk) 16:33, August 4, 2014 (UTC)
 * Yup. :) King2218 (talk) 16:40, August 4, 2014 (UTC)

k guys ive improved King's work and have proven the following:


 * 0 * 1 r

you're.so.pretty! 07:39, August 29, 2014 (UTC)


 * This reminds me of a bug on old Windows versions which makes the upper-right buttons of windows appear as "0 1 r", among other graphical glitches. So that was a theorem all along?!?!? -- ☁ I want more clouds! ⛅ 12:16, August 29, 2014 (UTC)

Bachmann OCFs
It took a while, but I finally located [http://www.ngzh.ch/pdf/?file=%2Farchiv%2F1950_95%2F95_2%2F95_14.pdf&title=Die%20Normalfunktionen%20und%20das%20Problem%20der%20ausgezeichneten%20Folgen%20von%20Ordnungszahlen. the original paper] by Heinz Bachmann describing one of the first ever ordinal collapsing functions. There's one problem: it's in German.

Some help deciphering it would be appreciated. you're.so.pretty! 00:23, August 30, 2014 (UTC)


 * I can help you, if you want. Go to the wiki chat (not IRC) and we'll start. I'll join when I see you are in. Also, it looks nice. Wythagoras (talk) 16:48, August 30, 2014 (UTC)
 * Oh man, that'd be great! If you could find some way to decipher the psi/phi function in the paper and get a complete definition on ordinal collapsing function, I would probably love you forever you're.so.pretty! 19:57, August 30, 2014 (UTC)
 * Sorry, I've been super absent-minded and have been forgetting to open Wikia Chat. Even worse, our time zones are nine hours apart, so I've probably been asleep for most of the times you've been on and vice versa :c you're.so.pretty! 09:45, August 31, 2014 (UTC)
 * Well, you now went to sleep, and for me and Wyth it's around noon right now. LittlePeng9 (talk) 09:51, August 31, 2014 (UTC)

Friedman
Did you contact him? What did he say about other problem? Wythagoras (talk) 16:48, August 30, 2014 (UTC)


 * I had to restate the other question, because the way I stated it was a bit too vague. I'm waiting for a reply right now. LittlePeng9 (talk) 17:00, August 30, 2014 (UTC)
 * Hasn't he replied yet? Wythagoras (talk) 05:57, September 6, 2014 (UTC)
 * Nope ;-; LittlePeng9 (talk) 06:26, September 6, 2014 (UTC)

stackoverflow
I'm not surprised that the stackoverflow folks are picky about your question. (They always are.) Here's my advice: since you are talking about code, post actual code. This is probably the main reason it was suspended. Also, make sure to post the minimal amount of code necessary for a complete stranger to understand it. it's vel time 07:10, September 17, 2014 (UTC)

Editing blogs.
DONT. EDIT. http://googology.wikia.com/wiki/User_blog:Alejandro_Magno/My_ordinal_is_smaller_Remake EVER. AGAIN -- A Large Number Googologist -- 21:13, October 14, 2014 (UTC)

dude
i'm going to have to ask you to stop leaving comments on Alejandro's posts, or in general interacting directly with him. you're just stirring up trouble. it's vel time 21:36, October 14, 2014 (UTC)


 * Okay, I understand. Sorry for causing trouble. LittlePeng9 (talk) 04:23, October 15, 2014 (UTC)

w_1^ck = w_1
recall that the church-kleene ordinal is defined as the least ordinal that is not the order type of a computable well-ordering of a subset of the natural numbers, and that the first uncountable ordinal is defined as the least ordinal that is not the order type of any well-ordering of a subset of the natural numbers. is it possible for these to be equal in a "reasonable theory"? it's vel time 03:21, November 9, 2014 (UTC)