Addition, multiplication, and exponentiation on ordinals are defined by transfinite recursion and are non-commutative. Lexicographic sum/product, Cantor normal form α = ω^{β_1}·c_1 + ⋯ + ω^{β_k}·c_k, and ε_0 = sup{ω, ω^ω, ω^{ω^ω}, …}…
Addition, multiplication, and exponentiation on ordinals are defined by transfinite recursion and are non-commutative. Lexicographic sum/product, Cantor normal form α = ω^{β_1}·c_1 + ⋯ + ω^{β_k}·c_k, and ε_0 = sup{ω, ω^ω, ω^{ω^ω}, …}…