User blog comment:PsiCubed2/Help Me Understand Ordinals Beyond the BHO/@comment-30118230-20170220203230/@comment-5529393-20170307024951

Hello PsiCubed2 - I'm sorry that you've been having so much trouble. I've been meaning to write up more in the "Introduction to Collapsing Functions" article, that would go into more detail how things work. But, I haven't managed to do anything yet.

One nice thing about the ϑ function is that is 1-1; each ordinal in the range will be expressed as ϑ(a) for precisely one value of a. But yeah, that does mean it skips around.