zukenft wrote:this might be a good place to ask, as it has something to do with irrational numbers. what do you call a type of irrational number that can be 'defined'?

for example, 0.101001000100001... the number of zeroes increase every iteration. this sequence certainly do not repeat, but it is very easy to predict the nth decimal.

other example would be 0.122333444455555... (repeat the number by its value) 0.11235813... (fibonacci sequence)

maybe the term is 'programmable irrational'? I think once you define the number you can write a program to generate it.

The term is "computable", but that includes the traditional irrationals too - if you want you can write a program to generate sqrt(2) or pi (people have actually done that), it would just be a bit longer.

(Note that there is a slight complication there - in some cases, you might not be able to be sure that your next digits won't end up being a ludicrous amount of nines (or zeroes) in a row, perhaps much longer than the rest of your current digits, leaving you unable to easily determine what the actual next digit is if you're working approximately. Thpugh this is not a problem for sqrt(2) and pi (easily proven in the former case, known theorem in the latter), and is of course astronomically unlikely to ever happen anywhere else but hadn't been proven definitely.)

As it happens, due to some complicated math stuff (Goedel's theorems, mostly), it's actually possible to define a number that it's mathematically impossible to write a program for. (And there are of course many other such numbers that can't even be defined - at least not finitely.) The assorted omega numbers discussed here previously mostly work that way.