Just making sure this is clear: I don't actually guarantee any new features for this. This is just something I'm doing in my spare time (and sometimes I have other stuff I want to do), and also I'm not an expert on the stuff here; I'm only going to work on this if I'm sufficiently interested, have time, etc. I don't have an issue with suggesting features, as long as you understand that I don't have an obligation to add them.
ε₀: It's been a while since I worked on the ordinal numbers part, but from what I can remember, I had trouble finding information about how exactly to do what I'm trying to do here (take an arbitrary expression and simplify it to some canonical form); like, the definitions weren't worded in a way that makes this easy, and there were examples, but not enough to cover all the cases. I figured out enough to be confident about expressions involving ω, but not enough to be confident about expressions involving ε₀. (I could look at it again at some point, but again, I don't guarantee anything.)
ג_n: Gimel? I'm not familiar with that notation.
real number imprecision: because computers can't actually perform exact calculations on real numbers. I included "real numbers" mostly for completeness, but everything involving real numbers is still doing calculations using floating point numbers. I did start a rewrite that would give more exact answers *sometimes*, but I never got around to finishing it.