Visualization of tridecal using exponents. You can just barely see the power towers, as they are only a few pixels wide at this scale.
Tridecal is equal to \(\lbrace10,10,10 \rbrace\), \(10\lbrace\lbrace1\rbrace\rbrace 2\) or \(10\lbrace10\rbrace10\) (10 dodecated to 10) in BEAF[1] or 3 & 10, using the array of operator. The term was coined by Jonathan Bowers.
In up-arrow notation, the number is equal to \(10 \uparrow^{10} 10 = 10 \uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow 10\).
Tridecal is the tenth Ackermann number.
The term "Infinity Scraper", defined by Jonathan Bowers, refers to any number larger than tridecal.
Sbiis Saibian gave this number another name, deka-endekaxis[2]
Aarex Tiaokhiao calls this number doclsol and is equal to s(10,10,1,2) = s(10,10,10) in strong array notation.[3]
BlankEntity coined Void Stand for this number. [4]
"Fashion" view of tridecal using iterated power towers with arrows.
Etymology
The name of this number is based on tri- (three) and decal- (ten), meaning that there are 3 10's in the array.
Approximations in other notations
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(10 \uparrow^{10} 10\) (exact value) |
| Chained arrow notation | \(10 \rightarrow 10 \rightarrow 10\) (exact value) |
| Hyperfactorial array notation | \(12!9\) |
| Hyper-E Notation | E1#1#1#1#1#1#1#1#1#10 (exact) |
| Strong array notation | \(s(10,10,10) = s(10,10,1,2)\) (exact) |
| Fast-growing hierarchy | \(f_{11}(9)\) |
| Hardy hierarchy | \(H_{\omega^{11}}(9)\) |
| Slow-growing hierarchy | \(g_{\varphi(9,0)}(9)\) |
Sources
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
- ↑ https://sites.google.com/site/largenumbers/home/4-3/Hyper-E
- ↑ Tiaokhiao, Aarex. Part 1 (LAN) - Aarex's Googology (old). Retrieved 2021-03-14.
- ↑ BlankEntity. BlankEntity's Googology - Up-arrow notation level. Retrieved 10 June, 2022.
See also
Tritri series: tritri · tritet · tripent · trisept · tridecal · grand tridecal
Tetratri series: tetratri · supertet · general(plex)
Pentatri series: pentatri · superpent · pentadecal(plex)
Hexatri series: hexatri · superhex · hexadecal(plex)
Heptatri series: heptatri · supersept · heptadecal
Iteral series: superoct · octadecal · superenn · ennadecal · iteral · ultatri
Dupertri series: dupertri · duperdecal · truperdecal · quadruperdecal
Latri series: latri · emperal(plex) · hyperal(plex) · diteral(plex) · admiral
Dutritri series: dutritri · dutridecal
Dimentri series: dimentri · dulatri · trilatri · trimentri
Triakulus series: triakulus · tridecatrix
Big boowa series: big boowa · great big boowa · grand boowa
Tiaokhiao's extensions: trihex · trioct · triennet · triundecal · tridodecal · tritriplex · tritriplexian · grand tritri · tetrapent · tetrahex · grand tetratri · octatri · enneatri · decatri · undecatri · dodecatri
RedBandServerYT's extensions: tridecalplex
-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
