Tetratri

The tetratri is equal to \( \lbrace 3, 3, 3, 3 \rbrace = 3 \lbrace\lbrace\lbrace3\rbrace\rbrace\rbrace 3 \) (3 powerexploded to 3) in BEAF. It surpasses Graham's number, and is the smallest Bowersism that does so.

Tetratri can be constructed in 2-bracket operator notation using the following process:


 * \(t_1 = 3\)
 * \(t_2 = 3 \lbrace\lbrace3\lbrace\lbrace3\lbrace\lbrace3\rbrace\rbrace3\rbrace\rbrace3\rbrace\rbrace3\) (tritri)
 * \(t_3 = 3 \lbrace\lbrace3\lbrace\lbrace3\lbrace\lbrace\cdots\lbrace\lbrace3\rbrace\rbrace3\rbrace\rbrace3\rbrace\rbrace 3\) with \(t_2\) arrows
 * \(t_4 = 3 \lbrace\lbrace3\lbrace\lbrace3\lbrace\lbrace\cdots\lbrace\lbrace3\rbrace\rbrace3\rbrace\rbrace3\rbrace\rbrace 3\) with \(t_3\) arrows
 * etc.
 * Tetratri is \(t_{t_3}\).