User talk:Vel!/Archive 5

hello leave me a message please

You're welcome. King2218 (talk) 17:22, April 18, 2015 (UTC)

A Question
Why is your user photo...nothing?

-- From the googol and beyond -- 23:45, April 17, 2015 (UTC)
 * It's rebranded. AarexWikia04 (talk) 11:25, July 29, 2016 (UTC)

--
Who owns this wiki?24.34.11.217 19:17, June 21, 2015 (UTC)

There are a few possible answers: -SJ224 19:34, June 21, 2015 (UTC)
 * Vel!
 * No one
 * Everyone, excluding spambots and such


 * Technically Vel! is the creator and thus the owner, but it is a lot more of a public property than anyone's in particular. LittlePeng9 (talk) 20:08, June 21, 2015 (UTC)
 * This site is owned and operated by Wikia, Inc. Pages are the intellectual property of their authors, and licensed under CC-BY-SA 3.0. Images and media have varying licenses, ranging from fair use to public domain. -- vel! 03:41, June 23, 2015 (UTC)

Thanks for putting up all those images for the functions; they really bring an atmosphere to the articles! Also, the roast beef- PERFECTION xD QuasarBooster (talk) 21:43, July 19, 2015 (UTC)

I think they're a little silly, but they aren't over the top so I don't really have a problem with it. -SJ224 13:23, July 21, 2015 (UTC)


 * I especially like one here, it's a beautiful bird. LittlePeng9 (talk) 13:42, July 21, 2015 (UTC)

Your expectations should've grown over time
Regarding this and this edit, I think your (or perhaps our) expectations appear to be grown. I remember that you being the one who proposed to call the Takeuti-Feferman-Buchholz ordinal the "Holy–Shit ordinal". -- ☁ I want more clouds! ⛅ 07:20, August 28, 2015 (UTC)
 * You got me there. The intent of the first edit was to cut back on terms like "extremely fast-growing" which is true of, y'know, every function on the wiki. -- vel! 18:23, August 28, 2015 (UTC)

Rayo's number lower bound formula
I'm looking at this comment about Rayo's number:

Defining "(¬∃1(1∈2))" (10 symbols) puts a 0 in x2. Defining "(1∈2∧(¬∃1(1∈3∧(¬1=2))))" (23 symbols) puts a 1 in x3. Defining "(2∈3∧(¬∃1(1∈4∧((¬1=2)∧(¬1=3)))))" (32 symbols) puts a 2 in x4. Defining "(3∈4∧(¬∃1(1∈5∧((¬1=2)∧((¬1=3)∧(¬1=4))))))" (41 symbols) puts a 3 in x5. etc. AND-ing together n expressions takes an additional 3n - 3 symbols. 0 takes at most 10 symbols. 1 takes at most 3 + 23 symbols. 2 takes at most 6 + 23 + 32 symbols. 3 takes at most 9 + 23 + 32 + 41 symbols. etc. Therefore the number of symbols it takes to Rayo-name n is at most (9n2 + 43n)/2.

But the formula doesn't match the actual lengths of expressions needed. When n=0 we get (9n^2+43n)/2=0, not 10. You need 10 symbols to assert the existence of 0.

For n=1 I'm getting 26 vs. 36. You have to combine the two together to assert the existence of 1. As stated on the main page, the assertion for 1 is


 * (((¬∃3(3∈2))∧2∈1)∧(¬∃3(3∈1∧(¬3=2))))

which is a 10-symbol part "(¬∃3(3∈2))" plus a "(" and "2∈1)∧(¬∃3(3∈1∧(¬3=2)))" adding up to 23, plus the 3 symbols "( ∧ )" needed to put them all together: 10+3+23=36. (The parentheses are moved around a little, but not in a way that breaks the formula.)

Similarly for n=2, (9n^2+43n)/2 formula gives 61, but we actually need 10+23+32+6 = 71.

For n=3 I have 105 vs. 115.

So I want to add 10 to the formula and make it "(9n^2+43n)/2+10" or "(9n^2+43n+20)/2".

Mrob27 (talk) 17:58, February 1, 2016 (UTC)
 * Actually, I have thought up a way to define a natural number "n" in 42n+10 symbols, like this:


 * 0 is defined as ¬∃n(n∈a0)", and an+1 is recursively defined as: "... ∧ an∈an+1∧¬∃n(n∈an∧¬(n∈an+1))∧¬∃n(n∈an+1∧¬(n=an)∧¬(n∈an)"


 * This definition starts out slow (for n=1 we need 52 symbols as opposed to 36 symbols), but it overtakes the other way quite quickly at n=5. By n=10 we have 430 symbols in this definition, but 2610 symbols in the other definition. Maybe called Googology Noob (talk) 12:23, February 27, 2016 (UTC)


 * @Googology Noob I honestly don't remember where we got that convention from, and I can't find a reference at the moment, but for Rayo's definition we always took the encoding of numbers as \(0=\{\},1=\{\{\}\},2=\{\{\{\}\}\},3=\{\{\{\{\}\}\}\}\dots\), while your definition works if we use a different convention (von Neumann ordinals). LittlePeng9 (talk) 14:03, February 27, 2016 (UTC)


 * If so, we have an even simpler definition!


 * 0 is defined as "¬∃n(n∈a0)" and an+1 is recursively defined as "...∧an∈an+1∧¬∃n(n∈an+1∧¬(n=an))". This definition takes only 20n+10 symbols, so the bound is improved even more! Maybe called Googology Noob (talk) 16:16, February 27, 2016 (UTC)


 * Actually, never mind what I said above; after taking a better look at formulas Mrob quoted I'm pretty sure that the way of encoding numbers as sets is actually via von Neumann ordinals. In either way, nice job on getting linear bounds, although they will have worse constants than claimed ones, because FOST requires more parentheses than you use in these formulas. LittlePeng9 (talk) 17:22, February 27, 2016 (UTC)


 * @Mrob27 Sorry no one addressed the issue before. Indeed you are right, and the derivation in the article seems to forget about the initial 10 characters we need to define 0. I am going to correct this.
 * Also, next time, please don't use user pages to talk about contents of a single article, but instead use a respective talk page, like this one. LittlePeng9 (talk) 14:03, February 27, 2016 (UTC)

We got Discord server!
Horray! AarexWikia04 (talk) 01:46, July 25, 2016 (UTC)
 * No thanks. -- vel! 07:19, July 29, 2016 (UTC)
 * Sorry, the invite expired. Do you want me to send you the invite, or you don't want discord server on Googology Wiki? -- From the googol and beyond -- 22:04, July 29, 2016 (UTC)

About "i'm going to delete them all"
On a comment on this blog post, you said that you're going to delete all those new pages created during your absense. I'm genuinely concerned about this. Are you being serious? Or are you just pulling our leg? -- ☁ I want more clouds! ⛅ 15:43, July 29, 2016 (UTC)
 * lol just wanted to see what would happen if i said that -- vel! 21:02, August 19, 2016 (UTC)