Veliki chisla chisla sho znachno bilshi nizh ti yaki zazvichaj vikoristovuyutsya v povsyakdennomu zhitti napriklad u prostomu rahunku chi groshovih operaciyah chasto z yavlyayutsya v takih oblastyah yak matematika kosmologiya kriptografiya ta statistichna mehanika Gugologiya rozdil matematiki ob yektami yakogo ye veliki chisla i yih nomenklatura 1 2 Termin buv utvorenij yak kombinaciya sliv gugol klasichne velike chislo i logos vchennya Zmist 1 Istoriya 2 Spisok gugologizmiv 3 Div takozh 4 PrimitkiIstoriya RedaguvatiIII st do n e Arhimed u svoyij praci Psammit predstaviv poznachennya sho dozvolyaye zapisuvati chisla do 10 8 10 16 displaystyle 10 8 times 10 16 nbsp 3 I stolittya V buddistskomu svyashennomu teksti Avatamsaka sutra bulo zgadano chislo 10 10 32 displaystyle approx 10 10 32 nbsp 1928 rik Vilgelm Akkerman opublikuvav svoyu funkciyu 1940 rik Edvard Kazner opisav chisla gugol 10 100 displaystyle 10 100 nbsp ta gugolpleks 10 10 100 displaystyle 10 10 100 nbsp 4 1947 rik Ruben Gudshtejn dav najmenuvannya operacij tetraciyi a b displaystyle a uparrow uparrow b nbsp pentaciyi a b displaystyle a uparrow uparrow uparrow b nbsp ta geksaciyi a 4 b displaystyle a uparrow 4 b nbsp 5 1970 rik S Vajner dav viznachennya shvidkozrostayuchoyi iyerarhiyi 6 1976 rik Donald Knut vinajshov notaciyu Knuta 7 mezha w displaystyle omega nbsp u terminologiyi shvidkozrostayuchoyi iyerarhiyi 1977 rik M Gardner v zhurnali Scientific American opisav chislo Grema 8 G g 64 f 64 4 displaystyle G g 64 f 64 4 nbsp de f n 3 n 3 displaystyle f n 3 uparrow n 3 nbsp Funkciya g n displaystyle g n nbsp maye shvidkist rostu poryadku w 1 displaystyle omega 1 nbsp 1983 rik bula vinajdena notaciya Shtejngauza Mozera 9 mezha w displaystyle omega nbsp 1995 rik D Konvej vinajshov lancyugovu strilochnu notaciyu mezha w 2 displaystyle omega 2 nbsp 2002 rik Dzhonatan Bauers opublikuvav svoyu notaciyu masivu mezha w w displaystyle omega omega nbsp i rozshirene poznachennya masivu mezha w w w displaystyle omega omega omega nbsp U 2007 roci Bauers viznachiv she bilshe svoyeyu duzhoyu poznachennya BEAF cya notaciya dobre viznachena do e 0 displaystyle varepsilon 0 nbsp chisla sho perevishuyut cej riven viklikayut superechlivist ocinok H Fridman en dav viznachennya funkciyi TREE n sho maye shvidkist zrostannya 8 W w w displaystyle theta Omega omega omega nbsp 2011 rik S Sajbian S Saibian zaproponuvav giper E poznachennya mezha w displaystyle omega nbsp v 2013 roci stvorenu na yiyi osnovi kaskadnu E poznachennya 10 11 mezha e 0 displaystyle varepsilon 0 nbsp i v 2014 roci rozshirenu kaskadnu E poznachennya mezha f w 0 0 displaystyle varphi omega 0 0 nbsp Spisok gugologizmiv RedaguvatiMatematichni ob yekti sho mayut vidnoshennya do gugologiyi zokrema veliki chisla nazivayutsya gugologizmami V danij chas najmenuvannya dani dlya dekilkoh tisyach chisel perevazhayuchih gugol Nizhche navedeno spisok deyakih gugologizmiv ta yih virazhennya v najbilsh vidomih notaciyah 12 Pered virazom v tij notaciyi v yakij chislo bulo zapisano avtorom stoyit znak rivnosti virazhennya dlya togo zh chisla v inshih notaciyah yavlyayut soboyu aproksimaciyi Im ya chisla Stepin desyati notaciya Knuta notaciya Konveya notaciya Bauersa notaciya Sajbiana shvidkozrostayucha iyerarhiyaGugol 10 100 displaystyle 10 100 nbsp 10 100 displaystyle 10 uparrow 100 nbsp 10 100 displaystyle 10 rightarrow 100 nbsp 10 100 displaystyle 10 100 nbsp E 100 displaystyle E100 nbsp f 2 324 displaystyle f 2 324 nbsp Gugolpleks 10 10 100 displaystyle 10 10 100 nbsp 10 10 100 displaystyle 10 uparrow 10 uparrow 100 nbsp 10 10 100 displaystyle 10 rightarrow 10 rightarrow 100 nbsp 10 10 100 displaystyle 10 10 100 nbsp E 100 2 displaystyle E100 2 nbsp f 2 2 324 displaystyle f 2 2 324 nbsp Giggol Giggol 10 10 10 10 10 100 desyatok displaystyle underbrace 10 10 10 cdots 10 10 text 100 desyatok nbsp 10 2 100 displaystyle 10 uparrow 2 100 nbsp 10 100 2 displaystyle 10 rightarrow 100 rightarrow 2 nbsp 10 100 2 displaystyle 10 100 2 nbsp E 1 100 displaystyle E1 100 nbsp f 3 100 displaystyle f 3 100 nbsp Gaggol Gaggol 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 desyatok 100 displaystyle left begin matrix amp amp underbrace 10 10 10 cdots 10 10 amp amp underbrace 10 10 10 cdots 10 10 amp amp underbrace quad quad vdots quad quad amp amp underbrace 10 10 10 cdots 10 10 amp amp text 10 desyatok end matrix right text 100 nbsp 10 3 100 displaystyle 10 uparrow 3 100 nbsp 10 100 3 displaystyle 10 rightarrow 100 rightarrow 3 nbsp 10 100 3 displaystyle 10 100 3 nbsp E 1 1 100 displaystyle E1 1 100 nbsp f 4 100 displaystyle f 4 100 nbsp Bugol Boogol 10 100 100 displaystyle 10 uparrow 100 100 nbsp 10 10 100 displaystyle 10 rightarrow 10 rightarrow 100 nbsp 10 10 100 displaystyle 10 10 100 nbsp E 100 100 displaystyle E100 100 nbsp f 101 100 displaystyle f 101 100 nbsp Chislo Grema 3 3 3 3 3 3 3 4 3 strilok 64 displaystyle left begin matrix amp amp underbrace 3 uparrow uparrow cdots uparrow uparrow 3 amp amp underbrace 3 uparrow uparrow cdots uparrow uparrow 3 amp amp underbrace quad quad vdots quad quad amp amp underbrace 3 uparrow uparrow cdots uparrow uparrow 3 amp amp 3 uparrow 4 3 text strilok end matrix right text 64 nbsp 3 3 65 2 displaystyle 3 rightarrow 3 rightarrow 65 rightarrow 2 nbsp 3 65 1 2 displaystyle 3 65 1 2 nbsp E 3 3 4 64 displaystyle E 3 3 4 64 nbsp f w 1 64 displaystyle f omega 1 64 nbsp Traddom Traddom 13 10 10 11 4 displaystyle 10 rightarrow 10 rightarrow 11 rightarrow 4 nbsp 10 10 3 2 displaystyle 10 10 3 2 nbsp E 10 10 4 displaystyle E10 10 4 nbsp f w 3 10 displaystyle f omega 3 10 nbsp Biggol Biggol 10 10 10 100 displaystyle 10 rightarrow 10 rightarrow 10 rightarrow 100 nbsp 10 10 100 2 displaystyle 10 10 100 2 nbsp E 100 100 100 displaystyle E100 100 100 nbsp f w 2 100 displaystyle f omega 2 100 nbsp Trultom Trultom 10 10 10 10 11 displaystyle 10 rightarrow 10 rightarrow 10 rightarrow 10 rightarrow 11 nbsp 10 10 10 3 displaystyle 10 10 10 3 nbsp E 10 4 displaystyle E10 4 nbsp f w 3 10 displaystyle f omega 3 10 nbsp Trugol Troogol 10 10 10 101 displaystyle underbrace 10 rightarrow 10 rightarrow cdots rightarrow 10 101 quad rightarrow nbsp 10 10 10 100 displaystyle 10 10 10 100 nbsp E 100 100 displaystyle E100 100 nbsp f w 2 100 displaystyle f omega 2 100 nbsp Chisla navedeni nizhche znahodyatsya vzhe za mezhami zastosuvannya notacij Knuta i Konveya Im ya chisla Notaciya Bauersa BEAF Notaciya Sajbiana Shvidkozrostayucha iyerarhiyaKvadrugol Quadroogol 10 10 10 10 100 displaystyle 10 10 10 10 100 nbsp E 100 100 displaystyle E100 100 nbsp f w 3 100 displaystyle f omega 3 100 nbsp Kvadreksom Quadrexom 10 10 10 10 10 10 displaystyle 10 10 10 10 10 10 nbsp E 10 10 displaystyle E10 10 nbsp f w 4 10 displaystyle f omega 4 10 nbsp Kvintugol Quintoogol 10 10 10 10 10 100 displaystyle 10 10 10 10 10 100 nbsp E 100 100 displaystyle E100 100 nbsp f w 4 100 displaystyle f omega 4 100 nbsp Gubol Goobol 10 100 1 2 displaystyle 10 100 1 2 nbsp 10 10 10 10 10 100 desyatok displaystyle underbrace 10 10 10 cdots 10 10 100 quad text desyatok nbsp E 100 99 100 displaystyle E100 99 100 nbsp f w 98 100 displaystyle f omega 98 100 nbsp Bubol Boobol 10 10 100 1 2 displaystyle 10 10 100 1 2 nbsp E100 100 100 f w w 99 100 displaystyle f omega omega 99 100 nbsp Trubol Troobol 10 10 10 100 1 2 displaystyle 10 10 10 100 1 2 nbsp E100 100 101 f w w w 2 100 displaystyle f omega omega omega 2 100 nbsp Kvadrubol Quadroobol 10 10 10 10 100 1 2 displaystyle 10 10 10 10 100 1 2 nbsp E100 100 101 f w w w 3 100 displaystyle f omega omega omega 3 100 nbsp Gutrol Gootrol 10 100 1 3 displaystyle 10 100 1 3 nbsp E100 100 100 f w w 2 100 displaystyle f omega omega 2 100 nbsp Gossol Gossol 10 10 1 100 displaystyle 10 10 1 100 nbsp E100 100 f w w 1 100 displaystyle f omega omega 1 100 nbsp Mossol Mossol 10 10 1 10 100 displaystyle 10 10 1 10 100 nbsp E100 100 f w w 2 100 displaystyle f omega omega 2 100 nbsp Bossol Bossol 10 10 1 10 10 100 displaystyle 10 10 1 10 10 100 nbsp E100 100 f w w 3 100 displaystyle f omega omega 3 100 nbsp Trossol Trossol 10 10 1 10 10 10 100 displaystyle 10 10 1 10 10 10 100 nbsp E100 100 f w w 4 100 displaystyle f omega omega 4 100 nbsp Dubol Dubol 10 100 1 1 2 displaystyle 10 100 1 1 2 nbsp E100 100 f w w 2 100 displaystyle f omega omega 2 100 nbsp Dutrol Dutrol 10 100 1 1 3 displaystyle 10 100 1 1 3 nbsp E100 100 100 f w w 2 2 100 displaystyle f omega omega 2 2 100 nbsp Kolossol Colossol 10 10 3 2 displaystyle 10 10 3 2 nbsp E10 10 f w w 3 10 displaystyle f omega omega 3 10 nbsp Terossol Terossol 10 10 4 2 displaystyle 10 10 4 2 nbsp E10 10 f w w 4 10 displaystyle f omega omega 4 10 nbsp Petossol Petossol 10 10 5 2 displaystyle 10 10 5 2 nbsp E10 10 f w w 5 10 displaystyle f omega omega 5 10 nbsp Gongulus Gongulus 10 10 100 2 displaystyle 10 10 100 2 nbsp E10 100 f w w 100 10 displaystyle f omega omega 100 10 nbsp Godtosol Godtothol 100 100 1 1 2 displaystyle 100 100 1 1 2 nbsp E100 100 f w w w w 100 displaystyle f omega omega omega omega 100 nbsp Godtopol Godtopol 100 100 1 1 1 2 displaystyle 100 100 1 1 1 2 nbsp E100 100 f w 6 100 displaystyle f omega uparrow uparrow 6 100 nbsp Godoktol Godoctol 100 100 0 1 1 1 1 2 displaystyle 100 100 0 1 1 1 1 2 nbsp E100 100 f w 9 100 displaystyle f omega uparrow uparrow 9 100 nbsp Dekotetrom Dekotetrom X 2 9 amp 10 displaystyle X uparrow 2 9 amp 10 nbsp E10 10 f w 10 10 displaystyle f omega uparrow uparrow 10 10 nbsp Goppatos Goppatoth 10 100 amp 10 displaystyle 10 uparrow uparrow 100 amp 10 nbsp E10 101 f e 0 101 displaystyle f varepsilon 0 101 nbsp Tesrakross Tethracross X 3 X 2 amp 100 displaystyle X uparrow 3 X 2 amp 100 nbsp E100 100 f z 0 100 displaystyle f zeta 0 100 nbsp Tesrakubor Tethracubor X 4 101 amp 100 displaystyle X uparrow 4 101 amp 100 nbsp E100 100 f h 0 100 displaystyle f eta 0 100 nbsp Tesrateron Tethrateron X 5 101 amp 100 displaystyle X uparrow 5 101 amp 100 nbsp E100 100 f f 4 0 100 displaystyle f varphi 4 0 100 nbsp Pentaksulum Pentacthulhum X X 1 2 amp 100 displaystyle X X 1 2 amp 100 nbsp E100 100 f G 0 99 displaystyle f Gamma 0 99 nbsp Geksaksulum Hexacthulhum X X 1 3 amp 100 displaystyle X X 1 3 amp 100 nbsp E100 100 f f 2 0 0 99 displaystyle f varphi 2 0 0 99 nbsp Godsgodgulus Godsgodgulus X X 1 99 amp 100 displaystyle X X 1 99 amp 100 nbsp E100 100 100 f f 98 0 0 99 displaystyle f varphi 98 0 0 99 nbsp TREE 3 f 8 W w w 3 displaystyle f theta Omega omega omega 3 nbsp Div takozh RedaguvatiShvidkozrostayucha iyerarhiya Chislo GremaPrimitki Redaguvati One Million Things A Visual Encyclopedia New York New York 10014 United States DK Publishing 2008 s 286 ISBN 978 0 7566 3843 6 Googology Arhiv originalu za 11 zhovtnya 2016 Procitovano 10 zhovtnya 2016 The Sand Reckoner Arenario Arhiv originalu za 7 serpnya 2016 Procitovano 8 zhovtnya 2016 Kasner Edward Newman James R 1940 Mathematics and the Imagination Simon and Schuster New York ISBN 0 486 41703 4 Arhiv originalu za 3 lipnya 2014 Procitovano 10 zhovtnya 2016 The relevant passage about the googol and googolplex attributing both of these names to Kasner s nine year old nephew is available in James R Newman red 2000 1956 The world of mathematics volume 3 Mineola New York Dover Publications s 2007 2010 ISBN 978 0 486 41151 4 Goodstein R L 1947 Lob M H and Wainer S S Hierarchies of Number Theoretic Functions I II A Correction Arch Knuth D E 1976 Mathematics and Computer Science Coping with Finiteness Arhivovano 24 serpnya 2013 u Wayback Machine Gardner M 1977 Mathematical games In which joining sets of points leads into diverse and diverting paths Arhivovano 19 zhovtnya 2013 u Wayback Machine Scientific American 237 5 18 28 doi 10 1038 scientificamerican1177 18 Steinhaus Moser Notation MathWorld Arhiv originalu za 13 zhovtnya 2016 Procitovano 10 zhovtnya 2016 Sbiis Saibian One to Infinity Arhivovano 13 zhovtnya 2016 u Wayback Machine Cascading E notation Arhivovano 13 zhovtnya 2016 u Wayback Machine Provereno 9 oktyabrya 2016 List of googologisms Arhivovano 21 listopada 2016 u Wayback Machine Provereno 10 oktyabrya 2016 Traddom Arhiv originalu za 11 zhovtnya 2016 Procitovano 10 zhovtnya 2016 Otrimano z https uk wikipedia org w index php title Veliki chisla amp oldid 37738829
