21/01/06 18:52:03.39 LJ6/y5JF.net
ハイパー原始数列を使って新しい順序数表記を考えてみた
0
1
2
3
[] = ω
[]+1 = ω+1
[]+2 = ω+2
[]+3 = ω+3
[]×2 = ω×2
[]×3 = ω×3
[]^2 = ω^2
[]^3 = ω^3
[]^[] = ω^ω
[]^[]^[] = ω^ω^ω
[]_0 = ε_0
[]_0^[]_0 = ε_0^ε_0
[]_0^[]_0^[]_0 = ε_0^ε_0^ε_0
[]_1 = ε_1
[]_2 = ε_2
[]_[] = ε_ω
[]_[]_0 = ε_ε_0
[]_[]_[] = ε_ε_ω
[]_(0,0) = ζ_0 = φ(2,0)
[]_(0,1) = ζ_1
[]_(0,2) = ζ_2
[]_(0,[]) = ζ_ω
[]_(0,[]_0) = ζ_ε_0
[]_(0,[]_[]) = ζ_ε_ω
[]_(0,[]_[]_[]) = ζ_ε_ε_ω
[]_(0,[]_(0,0)) = ζ_ζ_0
[]_(0,[]_(0,[]_(0,0))) = ζ_ζ_ζ_0
[]_(1,0) = φ(3,0)
[]_(2,0) = φ(4,0)
[]_([],0) = φ(ω,0)
[]_([]_0,0) = φ(ε_0,0)
[]_([]_[],0) = φ(ε_ω,0)
[]_([]_(0,0),0) = φ(ζ_0,0)
[]_([]_([]_(0,0),0),0) = φ(φ(ζ_0,0),0)
[]_(0,0,0) = Γ_0 = φ(1,0,0)
[]_(0,0,0,0) = φ(1,0,0,0)
[0] = []_(0,0,0,0,...) = ψ(Ω^ω)