- "Boilsol" redirects here. It is not to be confused with booilsol.
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Decker is 10 tetrated to 10 (or equivalently 10 pentated to 2), or {10,10,2} in BEAF.[1] The term was coined by Jonathan Bowers.
Informally, the number is one followed by "one followed by "one followed by "one followed by "one followed by "one followed by "one followed by "one followed by ten billion zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes" zeroes. It is also 10 pentated to 2, as \(n \uparrow^{k} n = n \uparrow^{k+1} 2\). The number's name is probably a reference to the SI prefix deca- for 10, which is itself derived ultimately from the Ancient Greek word δέκα, meaning 10.
In terms of recursion, decker is on par with the larger numbers giggol (10 tetrated to 100 = {10,100,2}) and grangol (E100#100), although decker is much smaller.
This number is also called dekalogue by Sbiis Saibian; it is E1#10 in Hyper-E notation.[2][3] This number can also be called megafugaten using Alistair Cockburn's megafuga- prefix.
Aarex Tiaokhiao calls this number digcol, bagiol or boilsol, and is equal to s(10,2,1,2) = s(10,10,2) in strong array notation.[4]
Username5243 calls this number doodcol or toodol, and is equal to 10[2]10 = 10[3]2 in Username5243's Array Notation.[5]
Approximations in other notations
| Notation | Approximation |
|---|---|
| Iterated scientific notation | \(10^{10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}}}\) (exact value) |
| Up-arrow notation | \(10 \uparrow\uparrow 10, 10 \uparrow\uparrow\uparrow 2\) (both exact values) |
| Chained arrow notation | \(10 \rightarrow 10 \rightarrow 2, 10 \rightarrow 2 \rightarrow 3\) (both exact values) |
| Steinhaus-Moser Notation | \(10[4]\) |
| BEAF | \(\{10,10,2\}, \{10,2,3\}\) (both exact values) |
| Hyperfactorial array notation | \(((((((((13!)!)!)!)!)!)!)!)!\) |
| Fast-growing hierarchy | \(f^9_2(30)\) |
| Hardy hierarchy | \(H_{\omega^2\times9}(30)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_0}(10)\) (exact value) |
| Joyce's More Generalized Exponential Notation | \(g(4, 2, 10)\) |
| Munafo's ASCII-lexicographic ordering | \(p8\_e010\_1\) (exact value) |
| Tetration notation | \(^{10}10\) (exact value) |
Visual representations
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
- ↑ Saibian, Sbiis. Hyper-E Numbers.
- ↑ Sbiis Saibian's Ultimate Large Numbers List
- ↑ Part 1 (LAN) - Aarex Googology (archived 2017-02-25)
- ↑ Part 1 - My Large Numbers
See also
-logue series: Dialogue · Trialogue · Tetralogue · Pentalogue · Hexalogue · Heptalogue · Octalogue · Ennalogue · Dekalogue · Endekalogue · Dodekalogue · Triadekalogue · Tetradekalogue · Pentadekalogue · Hexadekalogue · Heptadekalogue · Octadekalogue · Ennadekalogue · Icosalogue · Triantalogue · Terantalogue · Penantalogue · Exatalogue · Eptatalogue · Ogdatalogue · Entatalogue · Hectalogue · Chilialogue · Myrialogue · Chilia-chilialogue · Chilia-myrialogue · Myria-myrialogue · Dialogialogue · Sedeniadalogue · Guppylogue · Minnowlogue · Gobylogue · Gogologue · Ogologue · Googologue · Trialogialogue · Googolplexilogue · Tetralogialogue · Googolduplexilogue · Pentalogialogue · Googoltriplexilogue · Hexalogialogue · Heptalogialogue · Octalogialogue · Ennalogialogue · Dekalogialogue · Hectalogialogue · Chilialogialogue · Myrialogialogue · Octadialogialogue · Sedeniadialogialogue · Trialogialogialogue · Tetralogialogialogue · Pentalogialogialogue · Hexalogialogialogue · Heptalogialogialogue · Octalogialogialogue · Ennalogialogialogue · Dekalogialogialogue · Hectalogialogialogue · Chilialogialogialogue · Myrialogialogialogue · Octadialogialogialogue · Sedeniadialogialogialogue
-taxis series: Tria-taxis · Tetra-taxis · Penta-taxis · Hexa-taxis · Hepta-taxis · Octa-taxis · Enna-taxis · Deka-taxis · Hecta-taxis · Chilia-taxis · Myria-taxis · Chilia-chilia-taxis · Chilia-myria-taxis · Myria-myria-taxis · Sedeniadia-taxis · Googolia-taxis · Trialogia-taxis · Googolplexia-taxis · Tetralogia-taxis · Googolduplexia-taxis · Pentalogia-taxis · Googoltriplexia-taxis · Hexalogia-taxis · Heptalogia-taxis · Octalogia-taxis · Ennalogia-taxis · Dekalogia-taxis · Triataxia-taxis · Dekataxia-taxis · Hectataxia-taxis · Triataxiataxia-taxis · Dekataxiataxia-taxis · Hectataxiataxia-taxis
-petaxis series: Tria-petaxis · Tetra-petaxis · Penta-petaxis · Hexa-petaxis · Hepta-petaxis · Octa-petaxis · Enna-petaxis · Deka-petaxis · Hecta-petaxis · Chilia-petaxis · Myria-petaxis
-exaxis series: Tria-exaxis · Tetra-exaxis · Deka-exaxis · Hecta-exaxis · Chilia-exaxis · Myria-exaxis
-eptaxis series: Tria-eptaxis · Tetra-eptaxis · Deka-eptaxis · Hecta-eptaxis · Chilia-eptaxis · Myria-eptaxis
-octaxis series: Tria-octaxis · Tetra-octaxis · Deka-octaxis · Hecta-octaxis · Chilia-octaxis · Myria-octaxis
-ennaxis series: Tria-ennaxis · Tetra-ennaxis · Deka-ennaxis · Hecta-ennaxis · Chilia-ennaxis · Myria-ennaxis
-dekaxis series: Tria-dekaxis · Tetra-dekaxis · Deka-dekaxis · Hecta-dekaxis · Chilia-dekaxis · Myria-dekaxis
-endekaxis series: Tria-endekaxis · Tetra-endekaxis · Deka-endekaxis · Hecta-endekaxis · Chilia-endekaxis · Myria-endekaxis
-dodekaxis series: Tria-dodekaxis · Tetra-dodekaxis · Deka-dodekaxis · Hecta-dodekaxis · Chilia-dodekaxis · Myria-dodekaxis
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugaeleven · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten boogahundred · boogagoogol · boogagoogolplex
Gag: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex
