Omega and Epsilon

so if ω=2
then ω+1=3

ω+2=ω+ω=ω2=ω*ω=ω²=ω^ω=²ω=^ωω=ε₀=4

For this entire experiment I will be using only one of the definitions for these ordinals

^ωω=ε₀ as opposed to ε₀=ω^ε₀