I don’t think this conversation is being very productive so this is likely my final reply.
Just answer me a simple question.
? How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.
Just answer me a simple question.
How do the first 1000 naturals look like, after mixing supertask described above has finished its job,
You may say that this supertask is impossible.
You may say that there is no set of all naturals.
Whatever you think about it. Everything else is pretty redundant.
I don’t think this conversation is being very productive so this is likely my final reply.
The resulting pointwise limit exists, and it gives each positive integer a probability of zero. This is fine because the pointwise limit of a distribution on a countable set is not necessarily itself a distribution. Please take a basic real analysis course.