User:Alemagno12/Draft of a weakened yet fully functional catching function


 * ψ0(0) = (0,0)(1,1)
 * ψ0(1) = (0,0)(1,1)(1,1)
 * ψ0(ω) = (0,0)(1,1)(2,0)
 * ψ0(ψ0(0)) = (0,0)(1,1)(2,0)(3,1)
 * ψ0(Ω) = (0,0)(1,1)(2,1)
 * ψ0(Ω+1) = (0,0)(1,1)(2,1)(1,1)
 * ψ0(Ω2) = (0,0)(1,1)(2,1)(1,1)(2,1)
 * ψ0(Ωω) = (0,0)(1,1)(2,1)(2,0)
 * ψ0(Ω2) = (0,0)(1,1)(2,1)(2,1)
 * ψ0(Ω3) = (0,0)(1,1)(2,1)(2,1)(2,1)
 * ψ0(Ωω) = (0,0)(1,1)(2,1)(3,0)
 * ψ0(ΩΩ) = (0,0)(1,1)(2,1)(3,1)
 * ψ0(ΩΩ Ω ) = (0,0)(1,1)(2,1)(3,1)(4,1)
 * ψ0(ψ1(0)) = (0,0)(1,1)(2,2)
 * ψ0(ψ1(1)) = (0,0)(1,1)(2,2)(2,2)
 * ψ0(ψ1(Ω)) = (0,0)(1,1)(2,2)(3,1)
 * ψ0(ψ1(Ω2)) = (0,0)(1,1)(2,2)(3,2)
 * ψ0(ψ1(Ω2Ω2)) = (0,0)(1,1)(2,2)(3,2)(4,2)
 * ψ0(ψ1(ψ2(0))) = (0,0)(1,1)(2,2)(3,3)
 * ψ0(ψ1(ψ2(Ω3))) = (0,0)(1,1)(2,2)(3,3)(4,3)
 * ψ0(ψ1(ψ2(ψ3(0)))) = (0,0)(1,1)(2,2)(3,3)(4,4)
 * ψ0(C00(0)) = (0,0,0)(1,1,1)