I know this looks like spam, but please add:
Fibonacci {option: Starting numbers: _number_, _number_; presets: Fibonacci {1, 2}, Lucas {2, 1}} [The starting numbers (values of last 2 digits).]
Factors {option: Recursive: _checkbox_} [If it is recursive, the exponents are displayed in Factors notation.]
Transfinite ordinals {option: ω=: _number_} [Defines ω (the first transfinite ordinal) as a number, and then works upwards from there. ε_0 is defined to be ω^^ω (a power tower of ω ω's).]
Roman {option: Custom: _checkbox{yes @ Custom numbers: _list⁄_number_ = _text_⁄_, Allow subtraction rules: _checkbox_}_} [If custom numbers are turned on, you can set any number to any string, and toggle subtraction rules.]
Transfinite ordinals aren't a representation of the real numbers, so they wouldn't make sense for this page (there isn't really a way to show them in different bases etc.). However, I do have an ordinal number calculator: https://chridd.nfshost.com/calc/number-types#ord. It doesn't support ε₀ yet, I think because I couldn't figure something out.
I can't find information about that particular generalization of Fibonacci coding; I'll have to think more about whether that can work. (I know about the Lucas numbers, the question is whether/how they'd specifically work with Fibonacci coding.)
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.
I know this looks like spam, but please add: Fibonacci {option: Starting numbers: _number_, _number_; presets: Fibonacci {1, 2}, Lucas {2, 1}} [The starting numbers (values of last 2 digits).] Factors {option: Recursive: _checkbox_} [If it is recursive, the exponents are displayed in Factors notation.] Transfinite ordinals {option: ω=: _number_} [Defines ω (the first transfinite ordinal) as a number, and then works upwards from there. ε_0 is defined to be ω^^ω (a power tower of ω ω's).] Roman {option: Custom: _checkbox{yes @ Custom numbers: _list⁄_number_ = _text_⁄_, Allow subtraction rules: _checkbox_}_} [If custom numbers are turned on, you can set any number to any string, and toggle subtraction rules.]