I'm trying to solve 2 problems, but I'm having some issues and would appreciate help. Here are the questions and what I thought could be done:
1) A is the set of all series of numbers, where in an even place there is an even number, and in an odd place there is an odd number (for example, the series {8,3,2,5,0,1,28,...} is a valid member of A).
Is A of countable cardinality? If it is, find a one-to-one correspondence with the natural numbers.
My solution: I thought of sending a series, to a natural number. like, the example we got? I would send that series to the number 83250128 but I don't think thats a good solution...
2) B is the set of all series that only contain values that are prime numbers. Is B of countable cardinality? If it is, find a one-to-one correspondence with the natural numbers.