User blog comment:PsiCubed2/Counting with Ordinals/@comment-32876686-20171208202657/@comment-30754445-20171209155050

Remember that the goal here is to create an intuitive notation which does not rely on any prior understanding of ordinals. So whenever we use [x], x is always the "next" structure after the previous time we used [x].

Formally, we can define:

[x] = max (ω^x, x*ω)

Or alternatively:

[x] = (the smallest power of ω which is greater than x)

So for ε₀, we get ω^(ε₀+1) = ε₀ω.