The difference is that the probability of any given "real" number being used for anything, ever, or even being nameable, or even being potential covered by a naming scheme, is 0.
This is also true for countably infinite collections of real numbers.
Real numbers are unreal, at a scale incomprehensibly beyond the merely slightly hidden numbers like complex algebraics and the known transcendentals. Real numbers aren't numbers. R is a background continuum in which numbers exist. It is almost entirely void, yet contains an infinite collection of actual numbers.
Real numbers are unreal, at a scale incomprehensibly beyond the merely slightly hidden numbers like complex algebraics and the known transcendentals. Real numbers aren't numbers. R is a background continuum in which numbers exist. It is almost entirely void, yet contains an infinite collection of actual numbers.