Welcome!
Welcome to my googology website! For people who are dedicated to googology, large numbers and fast-growing functions. This website is for my googological notations and all of my defined numbers by HaydenTheGoogologist2009.
Note: Not everything in this site is made by me, I'll link to other sites (or Googology Wiki depending on the page) if it isn't owned by me.
Version: 8.3.1.0 (a)
Last updated on 25th April, 2023 10:04 PM (GMT+8)
Current status: None
Motivation: 100%
Quit SG (Standard Googology) bar: 0%
Quit FG (Fictional Googology) bar: -?????% (but I'm not good at making FG videos)
Inactive mode: Off
Updates
Recent updates
20th April, 2024: (v8.3.1.0 (a)) Happy 2nd anniversary to the site! However, it's 3 days late, and I don't know why I always forget that the website is created on 17th April.
5th April, 2024: (v8.3.1.0) I found out that I made a careless mistake: the numbers in Numbers by ChatGPT should be in the 83-ary number system, not 82-ary. That's why I changed the definitions for all 20 of the numbers.
4th April, 2024: (v8.3.0.0) Nowadays, ChatGPT is used everywhere in real life. But what about Googology? Today, I'll coin 20 numbers in Numbers by ChatGPT, which names are generated by ChatGPT!
1st April, 2024: (v8.2.0.0 (c)) Happy Easter (1 date late) and April Fools Day! Unfortunately, I don't have any pranks for you guys this year...
30th March, 2024: (v8.2.0.0 (b)) Since I'm back from my vacation, inactive mode is now off and I'll be active again!
27th March, 2024: (v8.2.0.0 (a)) Inactive mode is now on because I'll be on vacation starting tomorrow until 30th March, 2024.
17th March, 2024: (v8.2.0.0) Happy Saint Patrick's Day! To celebrate, I've coined 5 numbers in Saint Patrick's Day Numbers! Also, The Crystallization of Googology Wiki is officially completed!
14th March, 2024: (v8.1.2.14159265359) Happy Pi Day! As for that, I've changed the forth version number to be the first 11 decimal digits of pi (and I can do this because of a coincidence that the forth number is 1)
9th March, 2024: (v8.1.2.1) I'm now announcing that My BAN and SAN numbers is completed.
8th March, 2024: (v8.1.2.0) I've decided to cancel all numbers beyond Extendol-bisudex using EAN in SAN in My BAN and SAN numbers because some of the names are too hard to form. Also, I've replaced the numbers beyond pDAN with numbers that are easier to coin. And I won't coin anymore SAN numbers because I'm not motivated to do so.
Check out all updates here.
Who am I?
I'm HaydenTheGoogologist2009. My real name is Hayden Leung. I'm a boy who likes googology stuff and big numbers!
I also like to explore fast-growing functions and play games that have big numbers in it.
I'm both a Standard Googologist (SG-ist) and a Fictional Googologist (FG-ist).
Contents of my website
Introduction pages
Aims and Values - A page that lists my aims and values in the Googology Wiki and for myself.
Ultimate List of Numbers
Holiday numbers - These are my numbers created based on the holidays.
Chinese New Year Numbers - Happy Chinese New Year! I'm going to coin 11 Hong Kong street food numbers (all of them are salad numbers) every year!
Birthday numbers 2023 (completed) - It's my 14th Birthday! I'm going to create a list of numbers to celebrate my Birthday!
Saint Patrick's Day numbers - Happy Saint Patrick's Day! I'm going to coin 5 Saint Patrick's Day food numbers every year!
Cinco de Mayo numbers - Happy Cinco de Mayo! I'm going to coin 5 Mexican food numbers every year!
Tuen Ng Festival Numbers - Happy Tuen Ng Festival! I'm going to coin 5 festival-related numbers every year!
Mid-Autumn Festival numbers - Happy Mid-Autumn Festival! I'm going to coin 5 festival-related numbers every year!
For beginners - I found a bunch of documents for beginners. If you want to learn big numbers, why don't you start googology today?
Hayden's Big Numbers - A grand list of numbers using almost all notations in the googology wiki.
List of my prefixes (completed) - A list of my prefixes from 1 to 10^2,979.
Meet yourself in 105 degrees Celsius (completed) - How would you feel when you meet yourself at 105 degrees?
The Crystallization of Googology Wiki (completed) - I made this series to revive Redstonepillager's "Googology Wiki 15th anniversary special series" in a different way, as the series has been abandoned and deleted with reason "deleting the series after Christmas 2023 because the last few numbers of the series should be legitimately added until the Christmas Day in order to finalize the entire series which is a pure joke and is completely insincere, as well as numerous issues; however, the numbers will be kept and transferred to another page".
My Ember Arena numbers (completed) - I'll extend Sebastian Gomez05's Ember Arena with these numbers.
Cookies Inc. -illion numbers - Since the -illion numbers in the game “Cookies Inc.” are different from the official -illion names, I’ll compare them in the document inside.
My food based numbers (more numbers coming soon) - I think you guys might feel hungry now! :)
Numbers by ChatGPT (completed) - Nowadays, ChatGPT is used everywhere in real life. But what about Googology? Today, I'll coin 20 numbers, which names are generated by ChatGPT!
My infused numbers (completed) - Plugging the numbers into different notations! Insane, right?
My tier 10 -illion numbers (completed) - We've broke the limits of tier 4 -illions, time to go beyond!
Four seasons numbers (completed) - A number that will change definitions between seasons.
Goobol series (completed) - These are 'naive extensions' of the number goobol by putting Saibian's suffixes.
The number with the longest name ever in the entire everything ever (completed) - I'm now going to make a number again, and its name will be the longest in the entire everything ever.
My dynamic googolisms (completed) - My numbers that grows over time.
BAN and SAN numbers (completed) - A long list for my BAN and SAN numbers.
Popacthulhum regiment (abandoned) - Similar to Saibian's regiments, but using the dynamic googolism popacthulhum. Abandoned on 19th September, 2022 because I think it's going to take forever to complete the whole regiment.
My uncomputable numbers (completed) - I coined a number based on oblivion, because of that, the number is ill-defined.
霽霄's functions and numbers (completed) - This is a list of functions and numbers defined by 小魚七. Note that this page contains Chinese. All functions are ill-defined!
Notations
Hayden's Array Notation (abandoned) - My oldest array notation created on 12th April, 2022. The limit is approximated to ε0 in the fast-growing hierarchy. Abandoned on 15th September, 2022 because I created this notation when I was too immature.
Hayden's Extended Array Notation (abandoned) - An extension of Hayden's Array Notation created on 20th April, 2022. The limit is approximated to ϑ(ε(Ω + 1)) using Weiermann's ϑ in the fast-growing hierarchy. Abandoned on 15th September, 2022 because I created this notation when I was too immature.
Almighty Array Notation (abandoned) - My array notation created on 21st July, 2022. Abandoned this notation on October 23th, 2023 with the statement "This notation is a chaos, and I don't think it's possible to fix the entire notation. I should probably take a break from making notations..."
Periodic Table Notation (completed) - Created on 4th October, 2022. I decided to define the notation based on the periodic table, which is ordered according to the atomic number.
Megafactorial (completed) - Created on 2nd September, 2023. I've created a brand-new factorial-based function!
Experimental Works
These are my experimental works. They're most likely ill-defined as these works are very dumb. Some of them are created just for a 'joke'.
Memer Array Notation (completed) - Created on 1st April, 2023 for an April Fools prank. The dumbest notation I've ever made.
Others things related to standard googology
Analyses - I analysed some of the numbers and notations in the documents inside.
My Googological Ruler (completed) - I've made a googological ruler, a tool to compare big (both computable and uncomputable) numbers.
My Version of Sam's Number (completed) - Even though DeepLineMadom pointed out that Sam's number is not considered to be a defined number at all, I still want to explain my version of Sam's number just for a 'joke' for you guys.
Fixing Username5243's Array Notation (completed) - I decided to fix the ill-definedness of the UNAN since all 3 alternative definitions are all ill-defined. Unfortunately, DeepLineMadom pointed out that the fourth alternative (my) definition of UNAN proposed by me has some 'subtle problems'.
Fictional Googology
Number Goal Progression in History (completed) - To celebrate the 2 year anniversary of "Numbers 0 to 𝗔𝗕𝗦𝗢𝗟𝗨𝗧𝗘𝗟𝗬 𝗘𝗩𝗘𝗥𝗬𝗧𝗛𝗜𝗡𝗚 !!!", I've made the history of the famous number goals in the Fictional Googology based on when they were found.
The Longest S.N.T.A.G.U.O.M.S.E.M.G.E Chain Ever (completed) - I've created the longest S.N.T.A.G.U.O.M.S.E.M.G.E chain ever, combining the spam words in some videos in the numbers 0 to ??? series.
FG Community Related - These pages are not related to fictional googology itself, but the FG community!
My Thoughts on the Fictional Googology (completed) - As the FG (Fictional Googology) community is dying, I'll explain my thoughts on the Fictional Googology.
**DISCLAIMER: I actually like real googology more than fictional googology since the numbers in real googology actually make sense. If you don't like things that doesn't make sense and/or unreal, please don't click into the links above!**
Googology Wiki Related
These pages are not related to googology itself, but the Googology Wiki!
About Reliving C7X from an Admin (completed) - We held the admin election relieving C7X, I agree with the admin relieval before the admin election is holding by January 14, 2023. And I'm going to explain why.
Proposal for Modification of Policy in Googology Wiki:Policy#Analysis (completed) - We're currently holding the voting which decides that whether we should modify the policy in Googology Wiki:Policy#Analysis. In my decision, I agree to all 3 statements, but I have 2 questions.
Proposal for Reducing Minimum Block Span for the Warning Rule from 50 Years (completed) - We're currently holding the voting which decides that whether we should reduce the minimum block span for the warning rule from 50 years. In my decision, I agree to do so.
My OCF
Hayden's Extension of DeepLineMadom's extension of the extended Buchholz's function (ON HIATUS) - Time to extend the extended Buchholz's function to the unknowns!
Other googology sites
For beginners
The Googology Wiki (a collection of notations and numbers which have valid sources + more approximations)
Sbiis Saibian's excellent large number site: One to Infinity: A Guide to the Finite (a guided tour about number systems. There, he made a system, named Extensible-E, recommended for beginners)
Polytope sites by Jonathan Bowers (check out the Big Number Central for his googology works!)
Videos
Large Numbers Gradually Increasing by Douglas Shamlin Jr. (a series/playlist about numbers increasing, but only shown in Bird's array notation)
Numbers -Infinity to Infinity by NO! (a playlist about numbers increasing, since it's fun to watch, as well as it provides tips, hence it's recommended for beginners. However, this does not include all of the parts.)
1 to Absolute Infinity in One Video by NO! (a journey of numbers from 1 to Absolute Infinity. Note: the video is 14 hours long (combined from Large Numbers Gradually Increasing), so please watch it when you are free.)
Ultimate List of Large Numbers videos (they're originally by Douglas Shamlin Jr., but reuploaded by Dr2xmillion 2023 because the original videos were removed)
Numbers and notation sites (includes fictional googology sites)
XRQ CORPORATION's googology sites:
DeepLineMadom's googology sites:
SeveralLegend9998's googology site: SeveralLegend9998's Googology Series
NO!'s standard / fictional googology site: NO!'s Official Website
Jesse Kohn's standard / fictional googology site: Jesse's Official Site (beta of 10.0.0.0)
JoshuaDR.0809's fictional googology site: JoshuaDR.0809's Website
kien6886's fictional googology site: kien6886's Official Site
Main sites in googology wiki
Who Can Name the Bigger Number? by Scott Aaronson
Googology sites in other languages
大数入门 for those who know Chinese. Beware though, the article contains tons of mistakes.
Large Number in pixiv dictionary for those who know Japanese.
A document and a pie chart of the numbers I've coined
Source: https://docs.google.com/spreadsheets/d/1UrLkiNEGbOZqU-AfWF_LTT-LfvdV8i4KlF8-dGWpJN4/edit?usp=sharing
Social media links
YouTube channel - Eta Hyper Three Cardinal 2024
Instagram - hayden_leung_203
Reddit - Haydenism_Nomad_420
Googology Wiki page - HaydenTheGoogologist2009