a^a^a^… a

$latex boxed{a = a^{a^{a^ {{…}^{a}}}}}&fg=aa0000&s=3$ $latex text {…. [A] } $

$latex text {Let } a = sqrt {2} $

Method…: Wrong !!!

Method 1 : Rigorous!

1) Prove [A] Convergent ?

2) If converge, find Limit ?

https://v.ixigua.com/eUHCEkb/

Method 2: by RMI Homorphism