Is a random number chosen (or generated) at all?
See A random real is irrational. There is an argument that a random real number is not part of any countable set. Now see Science is countable, - all numbers that can be specified are countable. Can you say a number has been chosen if the number cannot be specified? It will always be "No, that's not the number" and never "Yes, that's the number". Can it then be called a chosen or generated number?
Pseudo-random numbers are generated, granted. But, it seems, not pure random numbers.