User blog:Alemagno12/An attempt at formalizing Username5243's Pi Notation

NOTE: This pi notation is slightly weaker to make the definition of transfinite fundamental sequences easier. First we have the base cases: Then, we have the cases for the successors of sequence ordinals: Then, we have the cases for limit ordinals:
 * π(0,x) = x+1
 * π(x,y) = π(x,y,ω)
 * π(z+1,0,0) = 0
 * π(z+1,0,x+1) = π(z,π(z+1,0,x))
 * π(z+1,0,x)[n] = π(z+1,0,x[n])
 * π(z+1,y+1,0) = π(z+1,y)+1
 * π(z+1,y+1,x+1) = π(z,π(z+1,y+1,x))
 * π(z+1,y+1,x)[n] = π(z+1,0,x[n])
 * π(z+1,π(a,b),x) = π(z+1,π(a,b,x))
 * [WIP]