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 (see my page on my Array Notation to see how it works).
I'll 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, a googolplex is 1 followed by a googol zeroes (or 1 followed by "1 followed by 100 zeroes" zeroes) = 10^10^100. A googolduplex is 1 followed by a googolplex zeroes = 10^10^10^100. As you can see, these are very large numbers, but they pale in comparison to whats coming next.
The Giggol group - this group includes {10,10,4}, giggol, giggolplex, giggolduplex, and the Mega (Mega can be seen on RobMunafo's web page). {10,10,4} (or 10 tetrated to 10) is 1 followed by "1 followed by "1 followed by " 1 followed by "1 followedby "1 followed by "1 followed by "1 followed by ten billion zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes. -YIKES, this is 10 to the power of itself 10 times. A giggol is 10 tetrated to 100 = {10,100,4} = 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. In other words a giggol is 10 to the power of itself 100 times. A giggolplex is 10 tetrated to agiggol = 10 {4} giggol = 10 {4} 10 {4} 100 = 10 to the power of itself a giggol times (or 10 to the power of itself "10 to thepower of itself 100 times" times). A giggolduplex is 10 {4} 10 {4} 10 {4} 100.
The Gaggol group - this group includes gaggol, gaggolplex, gaggolduplex, Megaston, tripent, and trisept. A gaggol is{10,100,5} = 10 {5} 100 (10 pentated to 100) = 10 tetrated to itself 100 times = 10 to the power of itself "10 to the power ofitself "10 to the power of itself "10 to the power of itself .........(say "10 to the power of itself" 98 times all together) .. "10 tothe power of itself - 1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1 followed by "1followed 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 {5} gaggol = 10 tetrated to itself a gaggol times. Gaggolduplex = 10 {5} gaggolplex. Megaston is mentioned on Rob's web page. Tripent = {5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4}5 {4} 5. Trisept = {7,7,7} = 7 {7} 7 (7 heptated to 7) = 7 hexated to itself 7 times = 7 pentated to itself "7 pentated to itself "7pentated to itself "7 pentated to itself "7 pentated to itself "7 pentated to itself 7 times" times" times" times" times" times. Ijust recently coined some new number names - geegol = {10,100,6}, geegolplex = {10,geegol, 6}, gygol = {10,100,7},gygolplex = {10,gygol,7}, goggol = {10,100,8}, goggolplex = {10,goggol,8}, gagol = {10,100,9}, gagolplex = {10,gagol,9}. Now that we got the small numbers out of the way, lets go for the smallest of the infinity scrapers. HUH?
The Tridecal - This number is {10,10,10} = 10 {10} 10 = 10 decated to 10 = 10 enneated to itself 10 times (10 {9} 10 {9} 10{9}..(ten times)..{9} 10) = 10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself "10 octated to itself 10 times" times" times" times" times"times" times" times" times. Where 10 octated to 10 = 10 heptated to itself 10 times - YIKES. As you can see, a tridecal(pronounced TRI da cal) is a horrendously huge number, also notice how the operators work (those like octation {8}, ordecation {10} - this can also be seen in more detail on my Array Notation page. Now imagine how enormous {3,3,27} is -this is 3 {27} 3 = 3 "27-ated" to 3 = 3 "26-ated" to itself 3 times = 3 "25-ated" to itself "3 "25-ated" to itself 3 times" times -which makes a tridecal look tiny.
The Boogol group includes boogol, boogolplex, and the Moser. A boogol = {10,10,100} = 10 {100} 10 = 10 hectated to 10(or 10 "100-ated" to 10). A boogolplex = {10,10,boogol} = 10 boogol-ated to 10 (or 10 "10 "100-ated" to 10"-ated" to 10) = 10{10{100}10} 10. The Moser is mentioned on Rob's web site and will fit among these.
The Corporal group includes Graham's number, the corporal, corporalplex, and Conway's 3 - 3 - 3 - 3 (where the dashrepresents an arrow). Graham's number and Conway's 3-3-3-3 are mentioned on Rob's site and are the largest finitenumbers mentioned in math literature (to my knowledge). 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) - keep in mind that 10 {10} 10 = tridecal, 10 {10 {10} 10} 10 = 10tridecalated to 10 - a corporal is much larger than Graham's number. A 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 {27} 3 = 3 {3 {3 {3...3 {3 {3} 3} 3...3} 3} 3} 3 (3 "27-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 Grand Tridecal = {10,10,10,2} = 10 {{10}} 10 = 10 expandodecated to 10 = 10 expandoenneated (or {{9}}) to itself 10times - this number dwarfs the previous numbers.
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 "27-ated" to 3 - then let 3 {3 {3 {3..... 3 {3 {3} 3} 3...3} 3} 3} 3 (with 3 "27-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 27-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 - YIKES! You can seewhy I call these "Infinity Scrapers"
The General group includes the general and the generalplex. 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). 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.
The Pentadecal group includes pentatri, pentadecal, pentadecalplex, hexatri, hexadecal, and hexadecalplex. Pentatri ={3,3,3,3,3}. Pentadecal = {10,10,10,10,10}. Pentadecalplex = {10,10,10,10,pentadecal}. Hexatri = {3,3,3,3,3,3}. Hexadecal = {10,10,10,10,10,10}. And hexadecalplex = {10,10,10,10,10,hexadecal} - these numbers are unspeakably huge - you may want to experiment with my array notation to get some feel of how big these are, they will make the generalplex look smaller than a microscopic dot.
The Iteral group includes iteral, iteralplex, and ultatri. The iteral = {10,10,10,10,10,10,10,10,10,10}. Ultatri (pronounced "ulTA 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 - this number shows up a lot when dealing with 3 containing multirowed arrays - just imagine it's size. Iteralplex = {10,10,10,10,10,10,...........,10,10,10} - contains an iteral10s - YIKES
using multirowed arrays, iteral =
{10,10}
{2 }
ultatri =
{3,27}
{2 }
iteralplex =
{10,iteral}
{2 }
- to be continued on page 2 -
Home Page 2 (where even BIGGER infinity scrapers are)
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