User blog comment:Syst3ms/Looking for some ideas/@comment-31966679-20180523230901

Coining names for numbers Give them the funniest names you can think of.

Extending on existing notations Whenever you see a notation/function, write it down on a list, then extend it, then post it as a blog post and ask how to extend it more like I did with my Generalized Factorial Function (now Generalized Factorial Notation, as you pointed out on my blog post).

You could also get inspiration from other functions/numbers. Like Rayo's function, but change first-order set theory to your own notation.