"Ronald Raygun" wrote
Agreed. [I was using integers/fractions to try to explain things more easily than with rationals/irrationals - I shouldn't have!]
"Ronald Raygun" wrote
I think it comes down to something called (something like) "enumeration" :- If you can produce a method which puts all the numbers (in the particular group which you are considering) into one list - eg 0, 1, 2, 3, 4, ... for whole numbers, or the list which you kindly provided for fractions - then they are of the same kind, the type which can be "enumerated".
However, there is no such possible list for irrational numbers - and hence they are "another kind".
"Ronald Raygun" wrote
;-)
It was this distinction between one kind of "infinity" and the bigger "infinity" that I was trying to alude to when comparing "keys" (which can be enumerated) with "algorithms" (which, I propose, cannot).