Talk: Hyper-E notation

The Hyper-E Notation page now have its own page, updated on August 21, 2012. There are some new numbers like Gaspgol and Ginorgol, and some names are changed. Now let's update the wiki! --Cloudy176 (talk) 08:37, August 26, 2012 (UTC)

While working on the pseudocode, I started thinking of computational complexity:

1. Ea is O(1).
2. Ea#b is O(b).
3. Ea#b#c is O(O(...O(O(b))...)) with c layers = O^c(b). I'll just write this as O^c.
4. Ea#b#c#d is ^dO.
5. Ea#b#c#d#e is O ↑↑↑ e.
6. etc.

I'm already abusing big O notation by treating it as a G function. FB100Z • talk • contribs 19:56, August 30, 2012 (UTC)

Hyper-E notation is not primitive recursive. The original version has growth rate comparable to the Ackermann function, which grows too fast to be primitive recursive. So Hyper-E notation grows too fast to be primitive recursive as well.

A primitive recursive function can be written using only fixed length loops. Deedlit11 (talk) 04:16, September 20, 2012 (UTC)

Extended Hyper-E notation didn't first appear on August 2012. It existed from the beginning. The August update on the Hyper-E notation page introduced more googologisms such as gaspgol, and changed name of some googologisms such as gugold or throogol. I want more clouds! 10:41, January 13, 2013 (UTC)

Sbiis Saibian extend his notation recently, all the way up to tetrational array-level and call it Cascade-E notation. I think there are good time for update. Ikosarakt1 (talk) 13:20, January 23, 2013 (UTC)

Hyper-F notation

Is it possible to devise a Hyper-F notation, which works like Hyper-E notation, but with all E's replaced by F's, and Rule 1 changed to Fx = x-th Fibonacci number? --84.61.136.79 18:53, September 16, 2014 (UTC)

Yes, it is. LittlePeng9 (talk) 19:17, September 16, 2014 (UTC)

But the real question is...why? it's vel time 19:32, September 16, 2014 (UTC)

What happens if we change E (or F) to BB, and Rule 1 to BBx = BB(x)? --84.61.136.79 19:35, September 16, 2014 (UTC)

A naive extension, since iterating over the busy beaver function doesn't really extend upon a function this powerful. Cookiefonster (talk) 20:19, September 16, 2014 (UTC)

Recursing a non-recursive function is pointless. it's vel time 23:27, September 16, 2014 (UTC)

Why must the number after the F in Hyper-F notation be larger than 5? --84.61.136.79 14:20, September 17, 2014 (UTC)

It's your notation. I don't think it really has to be. LittlePeng9 (talk) 14:24, September 17, 2014 (UTC)

Actually Peng, it does have to be above 5 - otherwise the function will not grow and stall at either 1 if the number is 1, 2, 3, or 4, or 5 if the number is 5. Cookiefonster (talk) 14:44, September 17, 2014 (UTC)

I see your point, but I think such values should be allowed anyway. Just because. -SJ224 14:50, September 17, 2014 (UTC)

BEAF takes degenerate value when first two entries are 2, but it's still allowed. LittlePeng9 (talk) 15:01, September 17, 2014 (UTC)

HEY GUYS THERES A THING CALLED INDENTATION it's vel time 19:51, September 17, 2014 (UTC)

WHO NEEDS THAT LittlePeng9 (talk) 20:02, September 17, 2014 (UTC)

@Peng if it's four or more entries only the first entry needs to be 4 Cookiefonster (talk) 19:53, September 17, 2014 (UTC)

Super-Hyper-E (E$)

Hyper-exponentiation (E#) is a replacement for Exponentiation, for use when there are too many E's.

bEs#h = bE... (h E's) ... Es, where b is the base, s is the significand, and h is the hypersignificand. Example: 2.5E4#2 = 2.5EE4 = 2.5E10,000

Extended Hyper-E (xE#) does something similar, for when there are many # hyperions, a number is added to denote how many there are.

bEs#^S @h = bEs#... (S #'s) ...#, where S denotes how many hyperions there are. Example: 2.5E4#^3 @2 = 2.5E4###2 = 2.5E4##2##2 =  2.5E4#2#2#2#2

Extensive use of xE# causes nesting, causing simple denoting of such things as 10[6]10 to look rather messy. Something similar with exponentiation would look like the following:

2.5E^12 @6 = 2.5E... (12 E's) ...E6

Super-Hyper-E is not necessarily a replacement for Extended Hyper-E, but another tool. Each tier multiplies with the exponent attached to the last (E#^2$4@2 = E########2) It adds new operations that mimic Hyper-E's Hyperion. Using subscripts in front of hyperions #\(_{n}\) can denote super-n-hyperions, though subscripts are not always available. Super-n-hyperions should be solved right to left, and smaller super-n-hyperions can appear behind the super-n-hypersignificand of larger ones. For following examples, these symbols shall be used.

• $ - Superhyperion (#\(_{1}\)) Superhypersignificands determine how many hyperions there are. Multiplies with any exponent attached to the hyperion.
• & - Megahyperion (#\(_{2}\)) Also known as Super-2-Hyperion. Megahypersignificands determine how many superhyperions there are. Multiplies with any exponent attached to the superhyperion.
• ¤ - Gigahyperion (#\(_{3}\))
• ╪ - Terahyperion (#\(_{4}\))
• ? - Petahyperion (#\(_{5}\))
• € - Exahyperion (#\(_{6}\))
• § - Zetahyperion (#\(_{7}\))
• ¶ - Yottahyperion (#\(_{8}\))

The system is infinite in length. There are not infinite symbols, as such, for using Super-n-hyperion, it is recommended that one must default to \(#{n}) or just #(n)

• Xonahyperion (#\(_{9}\))
• Vecihyperion (#\(_{10}\))
• Mecihyperion (#\(_{11}\))
• Duecihyperion (#\(_{12}\))
• Isohyperion (#\(_{20}\))
• Triacontahyperion (#\(_{30}\))
• etc..

Below are some xE# numbers denoted in E$:

• Godgahlah = E100#100$100 (100 E's, 100 #'s)
• Googahlah = E100#100$E100 (100 E's, E100 #'s)
• Greagahlah = E100#100$100&100¤100 (Note: this is assumed, as the given notation E100#^#100#100#100 confuses me)

Note: this is a draft. While useful to some people who are familiar with Extended Hyper-E notation, people who aren't familiar with it may be confused. Additionally, I am not entirely familiar with xE#, so some examples of xE# may be incorrect. If anyone wishes to add corrections or expansions, be my guest.

- Noobly Walker (talk) 18:13, April 5, 2020 (UTC)

Citation issue for C-code

It is known that the int-cast of pow function in C language does not coincide with the integer power. So, it seems that the coincidence of the return values of the C-code and the actual values of the function is non-trivial. Is there any proof or source? Since we are collecting sources and proofs for all non-trivial facts, I think that we need a source for the correctness of this code. Therefore I revert the addition of the code. Please revert my removal only when a source or a proof will be added.

p-adic 12:44, 23 December 2021 (UTC)

I don’t get it

Oversimplify it pls —Preceding unsigned comment added by Noahbloxian2010 (talk • contribs)