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.)
suggestion for addition: the plastic number base ("plastinary"?), which shares interesting properties with phinary.
> "It was proven by Aarts et al. (2001) that P and the golden ratio phi are in fact the only such numbers."
also corresponding mixed-base but we have perrin sequence and padovan sequence... maybe forget about this.
there might also be primorial base and its recursive version that seems somehow more elegant than factorial.
my idea about some "bijective factorial/combinatorial": 0->0 1->1 2->10 3->102 4->120 5->201 6->210 7->1023 8->1032 9->1203 ... but not sure if the shift-by-one is good.
also i'd prefer showing bijective binary by default.
also in case you're interested, the chinese ordinals 天干(decimal) 地支(duodecimal) 干支(sexagesimal, a tuple of two characters as a digit, starting from 甲子 乙丑, seems that's not yet supported in customization, unless unicode allocates 60 code points for them) may be used to form bijective systems. (though historically in reality the usage is just use one tuple as elements of (Z/60Z)+0.5)
in the binary section, a recent format called posit might be notable. though it's parameterized, there'll be some work on rounding and denormals. however there's plenty of official demo in js and i've heard that some hardware ALU has been produced.
further, i've made a dedicated Chinese huge number reading generator at farter.cn/number that supports several schemes. though it might be bit of out of scope, what i want to say here is that repeating the highest unit is widely accepted (in modern daily life, it's 亿. it's also acceptable to repeat 载 if we pretend to speak like our ancestors.)
about factors-like, here's my invention some years ago (turns out invented by someone else) oeis:A153013 (just ignore this)
finally, this page just completed (some of) my dream. it's just holy. i can safely delete my new folder now.
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.]wait wait wait doesn't explain enough.. ω+x = {same as before} ωy+x = yn+x ω^(z)y+x = yn^z+x [can be recursve in x] ε₀⁺ = {same as before}suggestion for addition: the plastic number base ("plastinary"?), which shares interesting properties with phinary. > "It was proven by Aarts et al. (2001) that P and the golden ratio phi are in fact the only such numbers." also corresponding mixed-base but we have perrin sequence and padovan sequence... maybe forget about this. there might also be primorial base and its recursive version that seems somehow more elegant than factorial. my idea about some "bijective factorial/combinatorial": 0->0 1->1 2->10 3->102 4->120 5->201 6->210 7->1023 8->1032 9->1203 ... but not sure if the shift-by-one is good. also i'd prefer showing bijective binary by default. also in case you're interested, the chinese ordinals 天干(decimal) 地支(duodecimal) 干支(sexagesimal, a tuple of two characters as a digit, starting from 甲子 乙丑, seems that's not yet supported in customization, unless unicode allocates 60 code points for them) may be used to form bijective systems. (though historically in reality the usage is just use one tuple as elements of (Z/60Z)+0.5) in the binary section, a recent format called posit might be notable. though it's parameterized, there'll be some work on rounding and denormals. however there's plenty of official demo in js and i've heard that some hardware ALU has been produced. further, i've made a dedicated Chinese huge number reading generator at farter.cn/number that supports several schemes. though it might be bit of out of scope, what i want to say here is that repeating the highest unit is widely accepted (in modern daily life, it's 亿. it's also acceptable to repeat 载 if we pretend to speak like our ancestors.) about factors-like, here's my invention some years ago (turns out invented by someone else) oeis:A153013 (just ignore this) finally, this page just completed (some of) my dream. it's just holy. i can safely delete my new folder now.