Before I go on to the next post, I want to piblish one of my works. It is a notation that I've been working on. It is also on the wiki I have posted a link in the previous post.
So Here it is : Prime Rules 1. Every Array/Integer - Every Array/Integer in the notation, the Psi (Ψ) is Needed. ( i.e. No Psi, then the whole array is wrong) ### Please note that in this post ONLY, array are right even without Psi. ### 2. Only One Entry - Ψn = n^n 2-1. Psi-Related - Ψnm = m^mn 3. Arrays - n_m_...% (% is the rest of the array) 3-1. Array Rule - Always calcluate from the back 3-2. Array Rule - Any Array calculates from the back. 3-3. Prime Array Rule - n_m = n^n^n^...^n (m times) (tetration) 3-4. 2<n Array Rule - n_m_o = n^n^...^n (m_o times) 4. Cerncerning 1, 0, and Infinity 4-1. If Ψn_m_1, The 1 may be cropped off (Ψn_m_1 = Ψn_m) 4-2. Ψ1_n_...% = 1 4-3. Infinity - The presence of Infinity ANYWHERE will cause the whole array to turn into Infinity (i.e.Ψn_m_..._(Infinity)_..% = (Infinity)) 4-4. Zero - Zeroes, like Infinity, in ANY array, will cause the array to become 1 (See i.e. on 4-3) 5. Special delimeters 5-1. Ψn#m = n_n_..._n (m times) 5-2. Ψn? = n_n-1_n-2_..._2_1 5-3. Array Marks (A,Y) (Based on BEAF's legions) 5-3-1. Simple Array Mark Rules - Ψ(main)A(array leader)n(Array Base)m(Array Children) 5-3-2. Extended Array Marks - ΨAAnm = ΨA(ΨAnm)m 5-3-3. Y Array - ΨYnm= ΨAA...AAnm 5-4. Bracker lines 5-5. Calculate the brackets first - Ψn_m/_m_n = Ψ(n_m)_(m_n) 5-6. "<>" Operators 5-6-1. Ψn<m = n#n#n...n#n (m times) 5-6-2. Ψn>m = m#m#m#...#m (n times) 5-6-3. Ψn>>m = n>n>n>...>n (m times) 5-6-4. ΨnA<mo= Ψn<<<......<<<o (m times) 5-7. n@ = n_n_..._n (n times) 6. Small Numbers 6-1. nm= Ψn_Ψn_Ψn_..._Ψn (m times) 7. Psi's 7-1. ΨΨn = Ψn_Ψn 7-2. ΨΨ...($ times)...Ψn = Ψn_Ψn_Ψn...Ψn ($ times) = $Ψn 7-2-1. nΨm ≠ n x Ψm *EXAMPLES* Googol = Ψ1010 = 10^10x10 = 10^100 Tritri = Ψ3_3_3) Decker = Ψ10_10 Gaggol = Ψ10#100 Googolplex ΨGoogol÷1010 = 10^10 x Googol÷10 = 10^Googol Enjoy and PLZ subscribe!!!!! ALL SOURCE OF GOOGOLOGY INFO COMES FROM THE GOOGOLOGY WIKI(A), OR SIMPLY https://googology.wikia.com/ Googology is a Branch of mathmatics dedicated to Very Large Numbers (or Integers).A Googol is 10 the 100th power. That means that It is 1 with a hundred zeroes after it. Actually, Google tried to name itself "Googol" (Portraying there are a Googol search results : This is 100% impossible :D), But a typing error led it's name to be GOOGLE. Googol+ and Googol Translate? Google is better :p The Number GOOGOL was coined by Edwatd Kasner's 9 year old nephew. It equals to 10 Duotrigintillion. Googol is what lead to Googology What "Big" Numbers do we know about and use fairly? A Million? A Billion? A Trillion? Or a Trevigintillion? Let's define and scale the -illion numbers by using a imaginary block. The block is 1 Cubic Centimeter, or 1cm on every side. What if there were a Million Blocks? A Million is 100 x 100 x 100, so a Milion blocks would make one big block 1 meter in every side. That's about six-tenth of your height. Fairly impressive. Now, what would a BILLION blocks look like? A Billion, is , 1000 x 1000 x 1000, so a Billion blocks would be 10 meters in every direction. That would be a size of a HOUSE. From Now on- I am only going to write the number, the size, and comparison points because things are getting a little bit too crazy. Trillion - 100 Cubic Meters - About one-fourth of the Empire Atate Building. Quadrilion - 1 Cubic Kilometer - About the size of a park. Height exceds the Burj Kalifa at 1 Km. Quintillion - 10 Cubic Kilometers - About the size of Mount Everest. Sextillion (No way related to sex) - 100 Cubic Kilometers - About the size of Ireland. Septillion - 1 Cubic Megameter - About the size of U.S.A if height scaled down. Octillion - 10 Cubic Megameters - About the size of the EARTH. Nonillion - 100 Cubic Megameters - About the size of Saturn. Decillion - 1 Cubic Gigameter - Abou the size of the SUN. A GOOGOL blocks would be MUCH bigger than the VISIBLE UNIVERSE! Now, We've talked about the numbers up to a Googol, and things are now exceding The scale of the VISIBLE UNIVERSE! But guess what? WE'RE NOT EVEN AT THE STARTING POINT OF LARGE NUMBERS! In the Next Post, We will talk about The Googol series, some notations, and Graham's Number. Thank you for your intrests and have a GOOD day :) |