User blog:MilkyWay90/"Proof" that lvl(n, w, 2) tends to zeta-0

\(lvl(1, \omega, 2) = \omega + 2\)

\(lvl(2, \omega, 2) = \omega * 2 = \omega + \omega\)

\(lvl(3, \omega, 2) = \omega ^ {2} = \omega * \omega = \underbrace{\omega + \omega + \ldots + \omega}_{\omega}\)

\(lvl(4, \omega, 2) = ^{\omega}\omega = \underbrace{\omega ^ {\omega ^ {\ldots ^ {\omega}}}_{\omega} = \varepsilon_{0}\)

\(lvl(4, \omega, 3) = \omega \uparrow \uparrow \omega \uparrow \uparrow \omega = \omega \uparrow \uparrow \varepsilon_{0}\)

\(\omega \uparrow \uparrow \varepsilon_{0} = \underbrace{\omega ^ {\omega ^ {\ldots ^ {\omega}}}}_{\varepsilon_{0}}\)

Turns out I was wrong (again). The level function can only head up to epsilon-0.