User blog comment:Vel!/Ordinals and arrow notation/@comment-5029411-20131211235541

e(0)^e(0) = (w^w^...)^(w^w^...) = w^{w^w^...*e(0)} = w^{{w^w^...}^2} = w^w^{e(0)*2}

e(0)^w^w^{e(0)*2} = {w^w^...}^{w^w^{e(0)*2}} = w^{w^w^...*w^{e(0)*2}} = w^w^{w^...+{e(0)*2}}

e(0)^^4 = w^w^{w^...+{w^...+{e(0)*2}}}

e(1) is approx w^^(w*2)

e(1)^e(1) = {e(0)^e(0)^...}^{e(0)^e(0)^...} = e(0)^{e(0)^e(0)...*e(0)^e(0)...} = e(0)^e(0)^{e(0)*2}

e(2) is approx w^^(w*3)

Wythagoras Win!