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From: ©2009 Martin Musatov. on 12 Sep 2009 00:37 1. visit http://meami.org 2. search the term: 2 N-1 = [ 3. click on the 1st hyperlink < the first hyperlink 3a. the 1st hyperlink reads: 'Factorial - Wikipedia, the free encyclopedia' 3b. the first hyperlink < the first hyperlink == - http://www.google.com/url?q=http://en.wikipedia.org/wiki/Factorial%23Alternative_definition&usg=AFQjCNFDywg2CDjiU1tNiYp0xuW23DRwTg&ei=ViKrSoywDZOusgPgnuiPBQ&sa=X&oi=section_link&resnum=1&ct=legacy === http://www.meami.org/?cx=000961116824240632825%3A5n3yth9xwbo&cof=FORID%3A9%3B+NB%3A1&ie=UTF-8&q=2+N-1+%3D+[&sa=Search#900 ==== 1a. Jump to Alternative definitionâ: n\mathrm{S}\!\!\!\!\! This sequence of superfactorials starts: 1\mathrm{S}\!\!\!\!\! 2\mathrm{S}\! \!\!\!\! 3\mathrm{S}\!\!\!\! ... en.wikipedia.org/wiki/Factorial =====Alternative definition===== [[Clifford Pickover]] in his 1995 book ''Keys to Infinity'' used a new notation, ''n$'', to define the superfactorial :<math>n\mathrm{S}\!\!\!\!\!\;\,{!}\equiv \begin{matrix} \underbrace { n!^{{n!}^{{\cdot}^{{\cdot}^{{\cdot}^{n!}}}}}} \\ n! \end{matrix}, \,</math> or as, :<math>n\mathrm{S}\!\!\!\!\!\;\,{!}=n!^{(4)}n! \,</math> where the <sup>(4)</sup> notation denotes the [[Tetration|hyper4]] [[operator]], or using [[Knuth's up-arrow notation]], :<math>n\mathrm{S}\!\!\!\!\!\;\,{!}=(n!)\uparrow\uparrow(n!). \,</ math> This sequence of superfactorials starts: :<math>1\mathrm{S}\!\!\!\!\!\;\,{!}=1 \,</math> :<math>2\mathrm{S}\!\!\!\!\!\;\,{!}=2^2=4 \,</math> :<math>3\mathrm{S}\!\!\!\!\!\;\,{!}=6\uparrow\uparrow6={^6}6=6^{6^{6^ {6^{6^6}}}}.</math> Here, as is usual for compound [[exponentiation]], the grouping is understood to be from right to left: :<math>a^{b^c}=a^{(b^c)}.\,</math> -doubleclick 'alternative definition' <1st hyperlink < 1st hyperlink @ http://www.meami.org/?cx=000961116824240632825%3A5n3yth9xwbo&cof=FORID%3A9%3B+NB%3A1&ie=UTF-8&q=2+N-1+%3D+[&sa=Search#900 + == the reality before you in your browser after you have double - clicked the text 'Alternative definitionâ' for the first time at this URL ©2009 Martin Musatov. Intellectual Property belongs to the poster.
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