Infinity Scrapers

And what are infinity scrapers? They are numbers which are so big, that even though they are finite, they seem to be reaching for infinity, like a sky scraper is a building that reaches for the sky. Actually that is an extreme understatement for most of these numbers - to be more accurate, these numbers are FAR beyond blasting off in a frenzied hurry towards infinity like its going out of style! - and that is still an understatement. I usually refer to numbers greater than a tridecal = {10,10,10} as infinity scrapers. The numbers will be described with my Exploding Array Function which is also called Array Notation. I've made some modifications since the first rendition of this page.

Lets start with the "smaller" numbers, such as a googol and a googolplex, then start going into larger and larger numbers like a gongulus and a golapulus.

The Googol Group - this group includes googol, googolplex, googolduplex, Skew's Number, and the large "illion" numbers. A googol is 1 followed by 100 zeroes = 10^100 = {10,100}, a googolplex is 1 followed by a googol zeroes (or 1 followed by "1 followed by 100 zeroes" zeroes) = 10^10^100 = {10,googol}. A googolduplex is 1 followed by a googolplex zeroes = 10^10^10^100. Of course you could keep going - googoltriplex, googolquadraplex, etc. As you can see, these are very large numbers, but they pale in comparison to whats coming next.

The Giggol Group - this group includes decker, giggol, tritri, giggolplex, giggolduplex, and the Mega (Mega can be seen on Rob Munafo's web page). Decker = {10,10,2} = 10^^10 (or 10 tetrated to 10) - it is 1 followed by "1 followed by "1 followed by " 1 followed by "1 followed by "1 followed by "1 followed by "1 followed by ten billion zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes. - in otherwords - 10 to the power of itself 10 times. A giggol is 10 tetrated to 100 = {10,100,2} = 1 followed by "1 followed by "1 fol .....(say "1 followed by" 98 times all together) .... lowed by 10 billion zeroes" zeroes" zeroes.....(say "zeroes" 98 times all together)... zeroes" zeroes. So a giggol is 10 to the power of itself 100 times. A giggolplex is 10 tetrated to a giggol = 10^^giggol = 10^^10^^100 = 10 to the power of itself a giggol times (or 10 to the power of itself "10 to the power of itself 100 times" times). A giggolduplex is 10^^10^^10^^100. A tritri = {3,3,3} = 3^^^3 = 3^^3^^3, this is 3 to the power of itself 7,625,597,484,987 times, it shows up a lot when playing with 3's in the exploding array function.

The Gaggol Group - this group includes gaggol, gaggolplex, gaggolduplex, Megaston, tripent, and trisept. A gaggol is {10,100,3} = 10^^^100 (10 pentated to 100) = 10 tetrated to itself 100 times = 10 to the power of itself "10 to the power of itself "10 to the power of itself "10 to the power of itself .........(say "10 to the power of itself" 98 times all together) .. "10 to the power of itself - 1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1 followed by 10 billion zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes - times" times" times" .... (say "times" 98 times all together) ..... "times" times!. A gaggolplex is 10^^^gaggol = 10 tetrated to itself a gaggol times. Gaggolduplex = 10^^^gaggolplex. Megaston is mentioned on Rob's web page. Tritet is {4,4,4} = 4^^^^4. Tripent is {5,5,5} = 5^^^^^5 = 5^^^^5^^^^5^^^^5^^^^5. Trisept is {7,7,7} = 7^^^^^^^7. Here's some other numbers - geegol = {10,100,4}, geegolplex = {10,geegol,4}, gigol = {10,100,5}, gigolplex = {10,gigol,5}, goggol = {10,100,6}, goggolplex = {10,goggol,6}, gagol = {10,100,7}, gagolplex = {10,gagol,7}. Now that we got the small numbers out of the way, lets go for the smallest of the infinity scrapers.

Tridecal - This number is {10,10,10} = 10 {10} 10 = 10 dodecated to 10 = 10 hendecated to itself 10 times (10 {9} 10 {9} 10 {9}..(ten times)..{9} 10) = 10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself "10 decated to itself 10 times" times" times" times" times" times" times" times" times. Where 10 decated to 10 is the old tridecal (the way I originally defined tridecal before making modifacations to array notation). As you can see, a tridecal (pronounced TRI da cal) is a horrendously huge number, also notice how the operators work (those like decation {8}, or dodecation {10} - this can also be seen in more detail on my Exploding Array Function page.

The Boogol Group - includes boogol, boogolplex, and the Moser. A boogol = {10,10,100} = 10 {100} 10 = 10 "102-ated" to 10. A boogolplex = {10,10,boogol} = 10 {10{100}10} 10. The Moser is mentioned on Rob's web site and will fit among these. Of course, there's the boogolduplex = {10,10,boogolplex}, boogoltriplex = {10,10,boogolduplex}, etc.

The Corporal Group - includes Graham's number, the corporal, corporalplex, and Conway's 3 - 3 - 3 - 3 (where the dash represents an arrow). Graham's number = {3,65,1,2} and Conway's 3-3-3-3 are mentioned on Rob's site. Corporal = {10,100,1,2} = 10 {{1}} 100 = 10 {10 {10 {10 {......10 {10 {10} 10} 10.....} 10} 10} 10} 10 (100 "10's" from center out) - note that 10 {10} 10 = tridecal and 10 {10 {10} 10} 10 = 10 tridecal+2ated to 10 - a corporal is much larger than Graham's number. Corporalplex = {10,corporal,1,2} = 10 {{1}} corporal = 10 {{1}} 10 {{1}} 100 = 10 {10 {10 {10 ......10 {10 {10} 10} 10....10} 10} 10} 10 (a corporal "10's" from center out). Conway's 3-3-3-3 is much larger than {3,3,2,2} but much smaller than {3,4,2,2} - {3,3,2,2} = 3 {{2}} 3 = 3 {{1}} 3 {{1}} 3 = 3 {{1}} 3{3{3}3}3 = 3 {{1}} 3 {tritri} 3 = 3 {3 {3 {3...3 {3 {3} 3} 3...3} 3} 3} 3 - (3 "tritri+2-ated" to 3 "3s" from center out). {3,4,2,2} = 3 {{2}} 4 = 3 {{1}} 3 {{1}} 3 {{1}} 3 = 3 {{1}} {3,3,2,2} = 3 {3 {3 {3....3 {3 {3} 3} 3....3} 3} 3} 3 - ({3,3,2,2} "3's" from center out).

The Biggol Group - includes grand tridecal, biggol, biggolplex, and biggolduplex. Grand Tridecal = {10,10,10,2} = 10 {{10}} 10 = 10 expandodecated to 10 = 10 expandoenneated (or {{9}}) to itself 10 times - this number dwarfs the previous numbers. Biggol was coined by Chris Bird to compare the googol, giggol, gaggol series to boogol - by adding biggol and baggol (seen later). Biggol = {10,10,100,2} and biggolplex = {10,10,biggol,2}.

Tetratri - (pronounced "teh TRA tree") = {3,3,3,3} = 3 {{{3}}} 3 = 3 powerexploded to 3, this number is even larger than 3-3-3-3-3 (Conway's Chained arrow notation). How big is this number, well - let 3 be on row 1 - then let 3 {3 {3} 3} 3 (3 "3s" from inside out)) be on row 2 - this is 3 "tritri+2-ated" to 3 - then let 3 {3 {3 {3..... 3 {3 {3} 3} 3...3} 3} 3} 3 (with 3 "tritri+2-ated" to 3 3s from center out) be on row 3 (get the picture), continue, to row 4, 5, 6, ......,all the way to row 3 {3 {3 {3... 3 {3 {3} 3} 3.... 3} 3} 3} 3 (with 3 tritri+2-ated to 3 3s from center out) - and this still aint it - this is only {3,3,3,2} = 3 {{3}} 3. Now consider 3 on row 1, and 3 {{3 {{3}} 3}} 3 on row 2, and 3 {{3 {{3 ....3 {{3 {{3}} 3}} 3 ....3}} 3}} 3 (with 3{{3{{3}}3}}3 3's from center out) on row 3, etc. Go to row 3 {{3 {{3 ....3 {{3 {{3}} 3}} 3... 3}} 3}} 3 (3{{3{{3}}3}}3 3s from center) - that is tetratri - GOLLY TELLY it's huge! You can see why I call these "Infinity Scrapers"

The Baggol Group - includes baggol, baggolplex, supertet, beegol, beegolplex, bigol, boggol, and bagol. Baggol = {10,10,100,3}, baggolplex = {10,10,baggol,3}, beegol = {10,10,100,4} - not to be confused with a dog, beegolplex = {10,10,beegol,4}, bigol = {10,10,100,5}, boggol = {10,10,100,6} - boggles the mind doesn't it, and bagol = {10,10,100,7} - what ever you do, don't eat this many bagels. Supertet = {4,4,4,4}.

The General Group - includes the general and the generalplex, as well as the troogol and troogolplex. General = {10,10,10,10} (can also be called tetradecal), this is also equal to 10 {{{{{{{{{{10}}}}}}}}}} 10, which is equal to 10 {{{{{{{{{{9}}}}}}}}}} 10 {{{{{{{{{{9}}}}}}}}}} 10 {{{{{{{{{{9}}}}}}}}}} 10 ..... {{{{{{{{{{9}}}}}}}}}} 10 -- (10 {{{{{{{{{{9}}}}}}}}}}ed to itself 10 times). The much smaller 10 {{{{{{{{{{1}}}}}}}}}} 4 = 10 {{{{{{{{{ 10 {{{{{{{{{ 10 {{{{{{{{{ 10 }}}}}}}}} 10 }}}}}}}}} 10 }}}}}}}}} 10 - imagine how big the general is!. The generalplex = {10,10,10,general} = 10 {{{{{{{......{{{{{ 10 }}}}}......}}}}}}} 10 - where the 10 is bracketed a general times. Troogol (coined by Bird) = {10,10,10,100} and troogolplex = {10,10,10,troogol}. This is getting close to the breaking point of Conway's Chained Arrow.

The Pentadecal Group - includes triggol, triggolplex, pentatri, traggol, traggolplex, treegol, superpent, trigol, troggol, tragol, pentadecal, quadroogol, and quadroogolplex. Triggol = {10,10,10,100,2} and triggolplex = {10,10,10,triggol,2}. Pentatri = {3,3,3,3,3}. Traggol = {10,10,10,100,3} and traggolplex = {10,10,10,traggol,3}. Treegol = {10,10,10,100,4}. Superpent = {5,5,5,5,5}. Trigol, troggol, and tragol = {10,10,10,100,n} where n=5,6, and 7 respectively. Pentadecal = {10,10,10,10,10}. Pentadecalplex = {10,10,10,10,pentadecal}. Quadroogol = {10,10,10,10,100} and quadroogolplex = {10,10,10,10,quadroogol}. These numbers are quite enormous.

The Iteral Group - includes quintiggol series, heptatri, supersept, heptadecal, sextoogol series, superoct, octadecal, septoogol, superenn, ennadecal, octoogol, iteral, and ultatri. Quintiggol, quintaggol, quinteegol, quintigol, etc = {10,10,10,10,10,100,n} where n=2,3,4,5,etc. Heptatri = {3,3,3,3,3,3,3} and supersept = {7,7,7,7,7,7,7}. Heptadecal, octadecal and ennadecal = {10,10,10,10,10,10,10}, {10,10,10,10,10,10,10,10}, and {10,10,10,10,10,10,10,10,10} respectively. Superoct and superenn = {8,8,8,8,8,8,8,8} and {9,9,9,9,9,9,9,9,9} respectively. Sextoogol, septoogol, and octoogol = {10,10,10,10,10,10,100}, {10,10,10,10,10,10,10,100}, and {10,10,10,10,10,10,10,10,100} respectively. The iteral (also called superdecal) = {10,10,10,10,10,10,10,10,10,10} = {10,10 (1) 2}. For a silly salad number, Wun = {1111!!,11!!!,11!,11!!!!,11!!!,11111!,1,1,1,11!,11} How many slices of pizza you want - wun. Ultatri (pronounced "ul TA tree) = {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3} - has 27 3s = {3,27 (1) 2} - just imagine it's size. We are now at the breaking point of linear arrays and at the very beginning of dimensional arrays.

The Goobol Group - includes goobol, dupertri, duperdecal, goobolplex, truperdecal, quadruperdecal, gibbol, latri, gabbol, geebol, gibol, gobbol, gabol, boobol, bibbol, babbol, beebol, bibol, bobbol, babol, troobol series, and quadroobol series. Goobol = {10,100 (1) 2} = {10,10,10,.....,10} - has 100 10's. Dupertri = {3,tritri (1) 2}. Duperdecal (also called iteralplex) = {10,iteral (1) 2}. Goobolplex = {10,goobol (1) 2} and truperdecal = {10,duperdecal (1) 2}. Quadruperdecal = {10,truperdecal (1) 2}. Gibbol = {10,100,2 (1) 2}. Latri = {3,3,3 (1) 2} - to get an idea of how big this is, consider this: start at 3, next go to {3,3,3} - which has 3 3's - this is tritri, next go to {3,3,3,3,.......,3} which has tritri 3's - this is dupertri, 4th go to {3,3,3,.....,3} - with dupertri 3's, and keep going until you get to the dupertri-ith level. Gabbol, geebol, gibol, gobbol, and gabol = {10,100,n (1) 2} where n=3,4,5,6, and 7. Boobol, bibbol, babbol, beebol, bibol, bobbol, and babol = {10,10,100,n (1) 2} where n goes from 1 to 7. The troobol and quadroobol series are similar - troobol, tribbol, trabbol, etc = {10,10,10,100,n (1) 2} and quadroobol, quadribbol, quadrabbol, etc = {10,10,10,10,100,n (1) 2} where n starts at 1. We can also coin a quintoobol series. These numbers can be thought of as the second level of linear arrays.

The Gootrol Group - includes gootrol, bootrol, trootrol, quadrootrol, gooquadrol, and booquadrol. Gootrol = {10,100 (1) 3}, bootrol = {10,10,100 (1) 3}, trootrol = {10,10,10,100 (1) 3}, and quadrootrol = {10,10,10,10,100 (1) 3}. Gooquadrol = {10,100 (1) 4} and Booquadrol = {10,10,100 (1) 4}. See if you can figure what the following numbers are: gitrol, gatrol, geetrol, gietrol, gotrol, gaitrol, quadreequadrol, gooquintol.

Emperal Group - includes the emperal, gossol, emperalplex, gossolplex, gissol, gassol, geesol, and gussol. Emperal = {10,10 (1) 10} and emperalplex = {10,10 (1) emperal}. Gossol = {10,10 (1) 100} and gossolplex = {10,10 (1) gossol}. Gissol, gassol, geesol, and gussol = {10,10 (1) 100,n} where n=2,3,4, and 5 respectively. Feel free to add -plex to any of the previous five - for instance a geesolplex = {10,10 (1) geesol,4}. We're finally hitting the second entry on the second row in the arrays.

Hyperal Group - includes hyperal, mossol, mossolplex, missol, massol, meesol, mussol, bossol, trossol, and quadrossol. Hyperal = {10,10 (1) 10,10} = 2^2 & 10 (2 by 2 array of tens). Mossol = {10,10 (1) 10,100} and mossolplex = {10,10 (1) 10,mossol}. Missol, massol, meesol, and mussol = {10,10 (1) 10,100,n} where n=2,3,4, and 5. Bossol, bissol, bassol, beesol, and bussol = {10,10 (1) 10,10,100,n} where n goes from 1 to 5. Trossol, trissol, trassol, treesol, and trussol = {10,10 (1) 10,10,10,100,n} n goes from 1 to 5. Quadrossol = {10,10 (1) 10,10,10,10,100} and quintossol = {10,10 (1) 10,10,10,10,10,100}. This group starts to fill up the second row in the arrays.

Admiral Group - includes diteral, dubol, dutrol, duquadrol, admiral, dossol, dutritri, and dutridecal. Here we fill out the third row. Diteral (prounounced DI ter al) = {10,10 (1)(1) 2} = {10,10,10,10,10,10,10,10,10,10 (1) 10,10,10,10,10,10,10,10,10,10}. Diteralplex = {10,diteral (1)(1) 2} = {10,10,......,10 (1) 10,10,......,10} - diteral 10's in each row. Dubol = {10,100 (1)(1) 2}, dutrol = {10,100 (1)(1) 3}, and duquadrol = {10,100 (1)(1) 4}. Admiral = {10,10 (1)(1) 10}. Dossol = {10,10 (1)(1) 100} and dossolplex = {10,10 (1)(1) dossol}. Dutritri = 3^2 & 3 = 3 by 3 array of 3's = {3,3,3 (1) 3,3,3 (1) 3,3,3} = {3,3 (2) 2}. Dutridecal = 3^2 & 10 = 3 by 3 array of 10's = {10,10,10 (1) 10,10,10 (1) 10,10,10} = {10,3 (2) 2}.

Xappol Group - includes the unspeakably huge xappol, xappolplex, and the grand xappol. Below is the xappol written out!

/10,10,10,10,10,10,10,10,10,10\

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 | = xappol - YIKES!!!!!

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

|10,10,10,10,10,10,10,10,10,10 |

\10,10,10,10,10,10,10,10,10,10/

A more compact way to write xappol (prounounced ZAP pul) is {10,10 (2) 2} = 10^2 & 10. Xappolplex = xappol^2 & 10 = {10,xappol (2) 2} - in otherwords it is a xappol by xappol array of tens! The grand xappol = {10,10 (2) 3} - these numbers are beginning to break past the planar (2-D) arrays - these numbers are larger than anyone can begin to imagine!!

Colossol Group - includes dimentri, colossol, colossolplex, terossol, terossolplex, petossol, petossolplex, ectossol, ectossolplex, zettossol, zettosolplex, yottossol, yottossolplex, xennossol, xennossolplex, and dimendecal. We are now going full force into the dimensional arrays. Dimentri = 3^3 & 3 = 3 x 3 x 3 array of 3's = {3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3 (2) 3,3,3 (1) 3,3,3 (1) 3,3,3} - think of a cube of 3's with 3 3's to the edge - that's the array. Colossol = 10^3 & 10 = {10,10 (3) 2} - here imagine a 10x10x10 cube of 10's. Colossolplex = colossol^3 & 10 = {10,colossol (3) 2} - here imagine a cube of tens that is so huge, there isn't enough universes to hold even a tiny fraction of it - it is a colossol by colossol by colossol cube of tens. Terossol = 10^4 & 10 = {10,10 (4) 2} - which is a 10 by 10 by 10 by 10 tesseract of tens. Terossolplex = terossol^4 & 10. Petossol is a size 10 penteract of tens - a 10^5 array of tens that is. Petossolplex is a size petossol penteract of tens. Ectossol is the value of a size 10 hexeract (six dimensional cube) of tens. Ectossolplex is an ectossol size hexeract of tens. Zettossol, yottossol, and xennossol are 7,8, and 9 dimensional size ten arrays of tens - in otherwords: 10^n & 10 = {10,10 (n) 2} where n=7,8,and 9 respectively. Dimendecal = 10^10 & 10's - which is a 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 array of 10's.

Gongulus Group - includes gongulus, gongulusplex, gongulusduplex, gongulustriplex, and gongulusquadraplex. Now the dimensional arrays are breaking at the seams. Gongulus is utterly unspeakably enormous - it is the result of solving a size ten 100 dimensional array of 10's (10^100 & 10 that is) = {10,10 (100) 2} - there will be a googol tens in the form of a hundred dimensional cube, which seems to never come to an end when trying to solve. Just to shake you up a bit, the much much much smaller number {10,10,3 (99) 2} can best be described as follows: 1) start with 10, 2) next get a size ten 99-D array, 3) now get a size X 99-D array where X is the result of stage 2, 4) now get a size Y 99-D array where Y is the result of stage 3,....go to stage ten, call that number T2, keep going - all the way to stage T2 - call that number T3, now keep going to stage T3 - call this number T4 - keep this trend up until you get to stage T10 - that will be {10,10,3 (99) 2} - notice how the 10,10,3 works like linear arrays but acting on expanding a 99-D array's size. Now consider {10^99 & 10 (99) 2} - MUCH larger now, but still NO where near a gongulus which is {10,10 (100) 2} = {10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10 (99) 10^99 & 10}. A gongulusplex is {10,10 (gongulus) 2} which is a size 10 - gongulus dimensional array of 10's! Gongulusduplex is {10,10 (gongulusplex) 2}, continue this trend for gongulustriplex and quadraplex.

Dulatri Group - includes dulatri, gingulus, trilatri, gangulus, geengulus, gowngulus, and gungulus. This is the beginning of tetrational arrays, actually the beginning of superdimensional arrays. Dulatri = {3,3 (0,2) 2} = {3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3}. the (0,1) separates dimensional groups, the same way (n) separates n-D structures. (0,1) can be thought of as (0+1*x) = (x) - which represents x^x structures being separated. (1,1) separates rows of dimensional groups, (n,1) separates n-D regions of dimensional groups. (0,2) separates groups of groups - so in the dulatri array {3,3 (0,2) 2} - the 2 is in the second group of groups, and the 3,3 is in the first group of groups. Dulatri then is a size 3 - x^2x array of 3's. {3,3 (0,1) 2} = 3^3 & 3 by the way. Gingulus = {10,100 (0,2) 2} = 100^100 array of D's where D is a 100^100 array of 10's. - so the gingulus array is a 100 dimensional array of 100-D dimensional groups, which is a size 100 - x^2x array of 10's. Trilatri = {3,3 (0,3) 2} = {A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (2,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A (1,2) A (0,2) A (0,2) A} where A represents "3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (2,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3 (1,1) 3^3 & 3 (0,1) 3^3 & 3 (0,1) 3^3 & 3" - this is a size 3 - x^3x array of 3's. Gangulus = {10,100 (0,3) 2}, geengulus = {10,100 (0,4) 2}, gowngulus = {10,100 (0,5) 2}, and gungulus = {10,100 (0,6) 2} - which is a size 100 - x^6x array of 10's.

Bongulus Group - this group includes bongulus, bingulus, bangulus, and beengulus, they are defined as {10,100 (0,0,1) 2), {10,100 (0,0,2) 2}, {10,100 (0,0,3) 2}, and {10,100 (0,0,4) 2} respectively. Bongulus uses a size 100 - x^x^2 array of 10's, beengulus uses a size 100 - x^(4x^2) array of 10's. The bongulus group is still using low order superdimensional arrays.

Higher Superdimensional Group - includes trimentri, trongulus, quadrongulus, and goplexulus. Trimentri = {3,3 (0,0,0,1) 2} which is a size 3 - x^(x^3) array of 3's - it is also a 1 trimensional array = {3,3 ((0,1)1) 2} - in otherwords a size 3 x^x^x array of 3's, a 3 tetrated to 3 array of 3's - a trimension is a dimension of dimension of dimensions. To help see this, let R represent a line (R for real numbers which is graphed like a line) - R^3 = 3 dimensions, R^R = R^R^1 - is 1 super dimension, R^R^4 = 4 super dimensions. R^R^R = R^R^R^1 = 1 trimension. R^R^R = R tetrated to 3 = {R,3,2}. Even though trimentri is defined with trimensions, it's array is of the higher superdimensional sizes. Trongulus = {10,100 (0,0,0,1) 2}, and quadrongulus = {10,100 (0,0,0,0,1) 2} = size 100 - x^x^4 array of 10's. Goplexulus = {10,100 (0,0,0,.......,0,0,1) 2} - where there are 100 0's - this is a size 100 - x^x^100 array of 10's.

Trimensional Group - includes goduplexulus (pronounced GO du PLEK su lus) - goduplexulus is {10,100 ((100)1) 2} which is a size 100 - x^x^x^100 array of 10's - following is another trimensional array example: {3,3 (4,2 (1) 6,7 (1) 7,8 (2) 7,8,5) 2} - the (4,2 (1) 6....8,5) represents separations between two x^(4+2x+ (6+7x)x^x + (7+8x)x^2x + (7+8x+5x^2)x^x^2) structures.

Higher Tetrational Group - includes gotriplexulus, goppatoth, and goppatothplex. Gotriplexulus = {10,100 ((0,0,0,....,0,0,1)1) 2 - with 100 0's - this is a size 100 - x^x^x^x^100 array of 10's. In dimensional arrays there are x^n structures (n being a positive integer), in superdimensional arrays, there are x^n structures (n being a positive valued polynomial = sum(i is a positive integer) mx^i), in trimensions there are x^n structures where n is a positive valued bipolynomial = sum(i in set of positive valued polynomials) mx^i, in quadramensions there are x^n structures where n is a positive valued tripolynomial, etc. Goppatoth = 10^^100 & 10's = size 10 - x^x^x^x^x^...........^x (100 x's) array of 10's, where goppatothplex is a 10^^goppatoth & 10's (& denotes "array of"). Goppatoth can also be wrote as {10,100,2) & 10 - which means a {10,100,2) array of tens = 10^^100 array of tens.

Pentation Group - includes triakulus, kungulus, and kungulusplex - even the arrays themselves are extremely difficult to imagine. Triakulus = {3,3,3} & 3 = 3^^^3 array of 3's - first one would need to invision a pentational array - and then fill this 3 pentated to 3 array full of 3's - and then solve it using my exploding array function - this number is utterly unspeakably huge. Kungulus = {10,100,3} & 10 = 10^^^100 array of tens. Kungulusplex = {10,kungulus,3) & 10 = 10^^^kungulus array of tens.

Higher Operation Groups - includes quadrunculus, tridecatrix, and humongulus. Quadrunculus = {10,100,4} & 10 = 10^^^^100 array of tens, tridecatrix = {10,10,10} & 10 = 3 & 10 & 10 = 10^^^^^^^^^^10 array of tens !!! - trying to solve this will cause anyone to get hopelessly lost trying to sort out all of the various array structures. Humongulus = {10,10,100} & 10 = 10^^^^^^^^^^^^`````^^^^10 (100 ^'s) array of tens. I suspect TREE(3) may land in this group or one of the adjacent groups.

Lineational Group - includes tetdecatrix, pendecatrix, hexdecatrix, hepdecatrix, ocdecatrix, endecatrix, lineatrix, and lineatrixplex. Tetdecatrix = {10,10,10,10} & 10, pendecatrix = {10,10,10,10,10} & 10, hexdecatrix = {10,10,10,10,10,10} & 10. Hepdecatrix = {10,10,10,10,10,10,10} & 10, ocdecatrix = {10,10,10,10,10,10,10,10} & 10, endecatrix = {10,10,10,10,10,10,10,10,10} & 10. Lineatrix = 10 & 10 & 10 = {10,10,10,10,10,10,10,10,10,10} & 10. Lineatrixplex = lineatrix & 10 & 10 = {10,10,10,10,10,.........lineatrix 10's........,10,10,10,10,10} & 10. The arrays that make these are so grand that you need linear array notation to describe the STRUCTURE. It appears that Friedmann's Tree function will lead to numbers in this area also, assuming that it grows as fast as the Small Veblen Ordinal on the FGH.

Golapulus Group - includes golapulus and golapulusplex. Golapulus = {10,100} & 10 & 10 = {10,10 (100) 2} & 10 - in otherwords it is a "10^100 array of tens" array of tens - a golapulusplex is a {10,100} & 10 & 10 & 10 = ""10^100 array of tens" array of tens" array of tens. To get an idea of the size of golapulus - consider the 10^100 array that generates gongulus, but dont solve it to a number - use this array to generate a structure - this "gongularray-space" structure will hold a gongulus entries when done - now fill THAT structure with tens. Here's a new number - Dekulus = 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10.

The Big Boowa - this number is outrageous - it needs to be represented with legion arrays. Big boowa = {3,3,3 / 2} - where {3,3 / 2} = 3&3&3 = triakulus. To get a feel of how big the big boowa is - think along these lines: stage 1: 3, stage 2: 3&3&3 = triakulus, stage 3: 3&3&3&3&3&.........&3 - a triakulus times, keep going to stage 3&3&3&3......3 - triakulus times: - this is the big boowa! {a,b / 2} = a&a&a&a&...&a b times. The great big boowa = {3,3,4 / 2}. The grand boowa = {3,3,big boowa / 2}.

Wompogulus Group - includes super gongulus and wompogulus. Super gongulus = {10,10 (100) 2 / 2} - used to be called bongulus (this name has been assigned to a different number). Wompogulus = {10,10 (10) 2 / 100}.

Guapamonga Group - includes guapamonga and guapamongaplex. Guapamonga = 10^100 legion array of 10^100 arrays of ten = {A/A/A/A/A/A/A/A/A/A(/2)A/A/A/A/A/A/A/A/A/A(/2)......(/99)....A/A} - where this array is a 10^100 array of A's divided by the legion bars and where A is a 10^100 array of tens. Guapamongaplex = 10^guapamonga legion array of 10^guapamonga arrays of ten.

The Big Hoss - "my goodness this number's huge - good gosh ol' mighty knows!, I sholy don't know wut ta tell ya!" as my late grandpa (who my brothers and I nicknamed "Hoss") would of said. This number is {100,100 //////.......///// 2} - with 100 /'s. We can call {big hoss, big hoss /////.......///// 2} - with big hoss /'s - the great big hoss. John Spencer suggested naming {100,100 /////......///// 100} - 100 /'s the grand hoss.

The Big Bukuwaha Group - during an e-mail session with Spencer, we came up with these numbers. Bukuwaha = {100,100 A 2} - where A is a 100^100 array of legion marks (/). Big Bukuwaha = {100,100 B 2} where B is a {100,100 A 2} array of "lugion" marks (\). Bongo Bukuwaha = {100,100 C 2} - where C is a {100,100 B 2} array of "lagion" marks (|). Quabinga Bukuwaha = {100,100 D 2} where D is a {100,100 C 2} array of "ligion marks" (-). Also in this area would be the Goshomity = {100,100 \\\...\\\ 2} (100 \'s) and the Good Goshomity = {100,100 \\\\....\\\\ 2} - with a goshomity \'s.

Meameamealokkapoowa Group - contains meameamealokkapoowa and meameamealokkapoowa oompa - I finally came up with working definitions after a few e-mails with Spencer who first asked for the definitions of these numbers, meameamealokkapoowa = {L100,10}10,10 and meameamealokkapoowa oompa = {LLL....a.....LLL,10}10,10 - where a = {L100,10}10,10 array of L's - trying to comprehend the size of this number is like trying to comprehend the size of God - see the array notations page to find out what these notations mean. It is pronounced (ME ya ME ya ME ya LOCK a POO wa) - where did I come up with this name you may ask, well actually the name came from the Crystal Dynamics game Gex - at the beginning of the tribal level, you hear a distant native yell out "meameamealokkapoowa" nobody knew what this unseen native was trying to say - until now.

Rayo Group - Far beyond the computable numbers, lays a number defined by Agust�n Rayo called Rayo's number = R(googol) where R is Rayo's function. This is so far beyond meamealokkapoowa oompa, that it may be thousands of groups ahead! Tyler Zahnke suggested using "Rayoplex" for R(Rayo) and Rayoduplex for R(R(Rayo)). We could even do BEAF style recursion on the Rayo function and it STILL wouldn't budge out of this group.

Oblivion Group - Oblivion is ONE terrible number! (assuming its definition really works!) , it is my attempt to sail past Rayo's number. The newly defined BIG FOOT would also land here -- and my attempt to beat it - Utter Oblivion.