User talk:Hyp cos

Can i ask who are you? JiawhienIsBackNoEvadeBlockOnceAgainIComeBack (talk) 09:10, October 1, 2013 (UTC)


 * Hyp cos. FB100Z &bull; talk &bull; contribs 19:02, October 1, 2013 (UTC)


 * The average of ex and its reciprocal. -- ☁ I want more clouds! ⛅ 03:18, October 3, 2013 (UTC)

SGH
Please look here. I gave reason why SGH is weaker than you think Wythagoras (talk) 19:00, October 16, 2013 (UTC)

SGH grows from outside --- \(g_{\theta(\Omega^\omega,1)}(n)\) stands above \(g_{p(SVO)}(n)\) for any function p which has lower level than SVO. So it's easy for SGH to grow from outside and hard to grow from inside. For example, \(g_{\theta(\Omega^{\omega+1})}(n)\) expands to \(g_{\theta(\Omega^\omega\theta(\Omega^\omega...\theta(\Omega^\omega)))}(n)\), \(g_{\theta(\Omega^\omega+1)}(n)\) expands to \(g_{\theta(\Omega^\omega,\theta(\Omega^\omega,...\theta(\Omega^\omega)))}(n)\), and even \(g_{\theta(\Omega^\omega,1)}(n)\) can expand to \(g_{\theta(\Omega^n,\theta(\Omega^\omega)+1)}(n)\).

However, many notations grow from inside, such as BEAF, BAN, HH, etc. .For example, \(H_{\omega^{\omega^\omega}+1}(n)=H_{\omega^{\omega^\omega}}(n+1)\), and {3,3,1,2}={3,3,{3,3,3}}. It's hard to compare them with SGH.

FGH can grows from outside or inside. \(f_{\alpha+1}(n)=f_\alpha^n(n)\). And there're 2 very different ways to get \(f_\alpha^2(n)\) from \(f_\alpha(n)\). One way is \(f_\alpha(n+1)\), \(f_\alpha(2n)\), ..., \(f_\alpha(p(n))\), ..., \(f_\alpha(f_\alpha(n))\), and thet other way is \(f_\alpha(n)+1\), \(2f_\alpha(n)\), ..., \(p(f_\alpha(n))\), ..., \(f_\alpha(f_\alpha(n))\). Thus, FGH becomes a general way to compare other notations. Notations growing from inside or outside suit. For comparison between FGH and SGH, we should grow FGH from outside and not inside. &#123;hyp&#60;hyp··cos&#62;cos&#125; (talk) 01:36, October 17, 2013 (UTC)
 * \(f_\alpha^2(n)\) just means \(f_\alpha(f_\alpha(n))\) and generally \(f_\alpha^n(n)\) is \(f_\alpha(f_\alpha(\cdots(f_\alpha(n))\cdots))\) with n f's. Ikosarakt1 (talk ^ contribs) 07:36, October 17, 2013 (UTC)

google site
DO you have your own google site about the large numbers? JiawhienIsBackNoEvadeBlockOnceAgainIComeBack (talk) 07:05, November 17, 2013 (UTC)

No. Actually I'm green to googology. hyp$hyp?cos&#38;cos (talk) 10:31, November 17, 2013 (UTC)

For Aarex
Make an extension of latest extension of Extended Up-arrow Notation. AarexTiao 01:50, December 1, 2013 (UTC)

Number navigator
Can you explain this a little more? FB100Z &bull; talk &bull; contribs 01:46, December 5, 2013 (UTC)

Number navigators in numbers such as Hyper-E numbers, Bowers' gongulus series, and lower hyperfactorial array numbers can be deleted because we can use the templetes as our new and powerful "number navigator". We can see other similar numbers in templetes. But, in nucleaxul we cannot delete it because there's no templete for nucleaxul numbers. If we delete it, we can't find numbers similar to nucleaxul on this page. hyp$hyp?cos&#38;cos (talk) 01:53, December 5, 2013 (UTC)
 * So why not just add a template? FB100Z &bull; talk &bull; contribs 02:44, December 5, 2013 (UTC)
 * Done! But there's still something wrong. In Extremexul template, the "Extremexul" in the first row under the title is bold, and it doesn't link to anywhere. However, in gigantixul template I newly add, the "Gigantixul" in the first row under the title links to page Gigantixul. But I don't know how to fix it. Okey now. Nothing serious in the new templates. hyp$hyp?cos&#38;cos (talk) 11:59, December 5, 2013 (UTC)

Extension of Nested Array Notation
Make an extension of Nested Array Notation
 * I found \(nR\{0\{1\text{^}\}*\} = nR\{0\{0\underbrace{**...**}_n\}\), \(nR\{0\{1\text{^}\}**\} = nR\{0\{0\underbrace{**...**}_n\{1\text{^}\}*\}*\}\), etc.


 * And \(nR\{0\{2\text{^}\}*\} = nR\{0\underbrace{\{1\text{^}\}...\{1\text{^}\}}_n*\}\), \(nR\{0\{3\text{^}\}*\} = nR\{0\underbrace{\{2\text{^}\}...\{2\text{^}\}}_n*\}\), etc.


 * \(\{0\{0\{0*\text{^}\}1\text{^}\}*\} = \{0\{0\{0\{...\text{^}\}1\text{^}\}1\text{^}\}*\}\)


 * The extension of NAN name is HNAN (Hyper-Nested Array Notation.) AarexTiao 14:47, December 29, 2013 (UTC)

Extra: Growth rate of PNAN = psi(X(e(0))) AarexTiao 02:08, December 27, 2013 (UTC)
 * I don't think so. First, we have different ideas from {0{0,1*}1} on. We know the nR{0{0,1*}1} and the nR{0{{0{0,1*}1}*}1} both have growth rate \(\psi(\psi_{I(1,0,0)}(0))=\psi(\psi_{\chi(M)}(0))\), but what's the equvalence? We know {0{1*}1} is equvalent to \(\psi_{I(\omega,0)}(0)\) (not \(\psi(\psi_{I(\omega,0)}(0))\) or \(I(\omega,0)\)), and {0{1*}2} is equvalent to \(\psi_{I(\omega,0)}(1)\), the {0{1*}0,1} is equvalent to \(I(\omega,0)\).
 * More, the {0{{0{1*}1}*}1} is equvalent to \(\psi_{I(\psi_{I(\omega,0)}(0),0)}(0)\),
 * the {0{{0{1*}1}*}0,1} is equvalent to \(I(\psi_{I(\omega,0)}(0),0)\),
 * the {0{{0{1*}0,1}*}1} is equvalent to \(\psi_{I(I(\omega,0),0)}(0)\),
 * and the {0{{0{1*}0,1}*}0,1} is equvalent to \(I(I(\omega,0),0)\).
 * The {0{{0{{0{1*}1}*}1}*}1} is equvalent to \(\psi_{I(\psi_{I(\psi_{I(\omega,0)}(0),0)}(0),0)}(0)\), and the {0{{0{{0{1*}0,1}*}0,1}*}0,1} is equvalent to\(I(I(I(\omega,0),0),0)\).
 * Now think of this: {0{0,1*}1} is the diagonalizer of {0{ ____ *}1}, so {0{{0{0,1*}1}*}1} is equvalent to \(\psi_{I(1,0,0)}(0)\), the {0{{0{{0{0,1*}1}*}1}*}1{{0{0,1*}1}*}1} is equvalent to \(\psi_{I(\psi_{I(1,0,0)}(0),1)}(0)\), the {0{{0{0,1*}1}*}2} is equvalent to \(\psi_{I(1,0,0)}(1)\), and the {0{{0{0,1*}1}*}0,1} is equvalent to \(I(1,0,0)\).
 * And the {0{0,1*}1} is equvalent to M, then.
 * So nR{0,1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\varepsilon_{M+1})}(0))\),
 * nR{0,0,1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\psi_{I_{M+1}}(0))}(0))\),
 * nR{0,0,0,1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\psi_{I(1,M+1)}(0))}(0))\),
 * nR{0{1*}1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\psi_{I(\omega,M+1)}(0))}(0))\),
 * nR{0{{0{{0{0,1*}1}*}1}*}1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\psi_{I(\psi_{I(1,0,0)}(0),M+1)}(0))}(0))\),
 * nR{0{{0{0,1*}1}*}1{0,1*}1} has growth rate \(\psi(\psi_{\chi(\psi_{I(M,1)}(0))}(0))\),
 * nR{0{0,1*}2} has growth rate \(\psi(\psi_{\chi(M_2)}(0))=\psi(\psi_{\chi(\psi_{I(1,0,M+1)}(0))}(0))\),
 * nR{0{0,1*}3} has growth rate \(\psi(\psi_{\chi(M_3)}(0))\),
 * nR{0{0,1*}{0{0,1*}1}} has growth rate \(\psi(\psi_{\chi(M_M)}(0))\),
 * So next to a comma means inaccessible, next to a {0,1*} means mahlo, and then next to a {0,2*} means compact. we can use {0{0,A*}1} for stage function of A, and the diagonalizer, {0{0,0,1*}1}, is the stage cardinal. Next to a {0,0,1*} means stage, so {0{0,0,1*}0,1} is inaccessible stage, {0{0,0,1*}0{0,1*}1} is mahlo stage, {0{0,0,1*}0{0,2*}1} is compact stage, {0{0,0,1*}0{0,0,1*}1} is stage stage. etc. hyp$hyp?cos&#38;cos (talk) 02:36, December 27, 2013 (UTC)
 * Well? {0{1,0,1*}1} is w-ex-stage, {0{{0,1},0,1*}1} is W-ex-stage, {0{{0,0,1},0,1*}1} is I-ex-stage, {0{{0{1*}1},0,1*}1} is I(w,0)-ex-stage, {0{{0{{0{0,1}1}*}1},0,1*}1} is chi(M)-ex-stage, {0{{0{0,1*}1},0,1*}1} is M-ex-stage, {0{{0{0,2*}1},0,1*}1} is compact-ex-stage, {0{{0{0,0,1*}1},0,1*}1}, and {0{0,1,1*}1} is stage-ex-...-ex-stage AarexTiao 02:50, December 27, 2013 (UTC)

In my system, stage-ex-stage-ex-...-ex-stage is just the first ordinal in the second row of n-dimensions, or psi(X(ww+12)) Wythagoras (talk) 07:42, December 27, 2013 (UTC)
 * I stronger than you! Check it out! AarexTiao 01:11, December 29, 2013 (UTC)
 * Well, if you have some strong ordinal notations, can you compare it to nested array notation? hyp$hyp?cos&#38;cos (talk) 02:27, December 29, 2013 (UTC)

HNAN II
Can you add Hyper-Nested Array Notation II on R function series? AarexTiao 15:17, February 1, 2014 (UTC)


 * click here AarexTiao 02:41, February 9, 2014 (UTC)

Thanks, Hyp cos. I see you have more experience with the categorization than I do.

Questions
Hello Hypcos. I would like to ask a few questions about your work with large numbers. I would like to ask a couple of questions about your website called WordPress Steps Toward Infinity. How come parts 8-12 don't work in your Strong Array Notation? Do parts 1-7 work in your Strong Array Notation? Does your R function work? Two people on this website told me that your R function has an infinite loop.
 * Some expressions in NDAN cause infinite loop, such as s(3,3{1(2(1)○△2)△3}2). That makes NDAN and beyond don't work. But I've just know what's the problem, and I'll fix it soon.
 * Parts 1-7 work, and they're as strong as R function.
 * But I don't know what's wrong with R function now. &#123;hyp/^,cos&#125; (talk) 00:42, July 1, 2016 (UTC)
 * iirc it was littlepeng9 who found the error. -- vel! 17:21, July 1, 2016 (UTC)
 * No, it wasn't me. For what I know it was Fluoroantimonic Acid. I have happened to meet him on IRC recently and I've asked him about this. I don't have access to logs right now, but he said that the flaw regarded an old version of the notation and that error isn't there anymore. I'm pretty sure Deedlit was there at the time of the conversation, so he might be able to provide logs. LittlePeng9 (talk) 19:51, July 1, 2016 (UTC)


 * I don't think the error was ever there. Here is the passage that FA thought meant there was a problem with the notation:


 * To solve s(a,b{1{2}1,2}2), we start the process, then meet case B2, then meet case B1. Before case B1 applies, the array is s(a,b{1{2}1,2}2{1{2}1,2}1); after case B1 applies, the array becomes s(a,a{1{2}b,1}2{1{2}1,2}1). Then rule 2a and 2b applies, so s(a,b{1{2}1,2}2) = s(a,a{1{2}b}2). What if we use the case B1 in Linear array notation? s(a,b{1{2}1,2}2) will be s(a,a{a{a}b}2). When a ≥ 3 and b ≥ 2, it’ll reduces to something containing {1{2}1,2} again – it can never be solved. So a change on case B1 is necessary.


 * But what Hyp Cos was saying was that if we used the version of B1 in "Linear array notation" in his "Extended array notation", then we would get an infinite loop, which is why he changed that particular rule for "Extended array notation". Deedlit11 (talk) 00:18, July 2, 2016 (UTC)


 * That cause only LAN will work and since NDAN is fixed, why DEN will have 2 types includes weak and strong? GoogleAarex2001 17:18, July 7, 2016 (UTC)

My feeling is that as a notation becomes more complex, the more necessary it becomes for someone to prove that it terminates. -- vel! 04:49, July 7, 2016 (UTC)

Question from Googleaarex
Is wDEN parts finally completed? GoogleAarex2001 23:32, July 11, 2016 (UTC)
 * It depends on how you define "wDEN parts". My plan for the next part is converting superscripts on droppers into a very special separator - that's a bit similar to "from mDEN to pDAN". &#123;hyp/^,cos&#125; (talk) 13:12, July 12, 2016 (UTC)
 * Since wDmEN is completed, what is your next part plan? AarexWikia04 (talk) 01:35, July 18, 2016 (UTC)
 * The case B3 in wDmEN makes it hard to extend. So I may make a new version of wDmEN before extend it. &#123;hyp/^,cos&#125; (talk) 01:39, July 18, 2016 (UTC)

Will you ever make number names past two-row arrays? Username5243 (talk) 01:43, July 18, 2016 (UTC)
 * Yes, but I'll finish it much later. &#123;hyp/^,cos&#125; (talk) 01:45, July 18, 2016 (UTC)