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Not to be confused with Conway's Tetratri.

The tetratri is equal to {3,3,3,3} = 3{{{3}}}3 (3 powerexploded to 3) in BEAF.[1] It can also be written 4 & 3, using the array of operator. The term was coined by Jonathan Bowers. It is larger than Graham's number and comparable to Sbiis Saibian's grinningolthra.

Tetratri can be computed in 2-bracket operator notation using the following process:
• $$t_1 = 3$$
• $$t_2 = 3 \{\{ 3 \{\{ 3 \}\} 3 \}\} 3$$
• $$t_3 = 3 \{\{ 3 \{\{ 3 \{\{ \cdots \{\{ 3 \}\} \cdots \}\} 3 \}\} 3 \}\} 3$$ with $$t_2$$ 3's from center out.
• $$t_4 = 3 \{\{ 3 \{\{ 3 \{\{ \cdots \{\{ 3 \}\} \cdots \}\} 3 \}\} 3 \}\} 3$$ with $$t_3$$ 3's from center out.
• etc.
• Tetratri is $$t_{t_{t_\cdots1}}$$, where there are $$t_{t_{t_1}}$$ t's.

## EtymologyEdit

The name of this number is based on tetra- (four) and tri- (three), meaning that there are four 3's in the array.

## Approximations Edit

Notation Approximation
Bird's array notation $$\{3,3,3,3\}$$ (exact)
Hyper-E notation $$E100\#\#100\#\#100\#\#4$$
Chained arrow notation $$3 \rightarrow 3 \rightarrow 3 \rightarrow 3 \rightarrow 4$$
X-Sequence Hyper-Exponential Notation $$3\{X^2\}3$$
Multivariable Ackermann $$A(1,0,0,3)$$
Fast-growing hierarchy $$f_{\omega^2}(3)$$

## Sources Edit

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.

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) · 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