[falserum]

1, 1.1, 1.01, 1.001, …

This will never reach 2, so it will not generate all real numbers. (Which was what parent was asking for, to recusively generate all R)

[ludston]

You can define a procedure that reaches 2 very trivially. e.g. you generate all possible 1 digit numbers, then 2 digit numbers, then 3 digit numbers, etc.

This is how natural numbers work in the first place. You're just adding a decimal point to all of the possible places it could go.

[falserum]

Thanks for reply.

When will this reach PI or e or sqrt(2)?

(There are infinitely many numbers that will not be reached by this procedure)

[kbrkbr]

If you could, you could use that procedure to create a mapping

1 => first step in the procedure 2 => second step ...

That in turn would mean that N and R have the same cardinality. This would be news.