- #1

jordi

- 197

- 14

By taking out an infinite subset to the natural numbers (the odd naturals), we get an infinite subset, the even numbers, which has the same size, aleph_0 (e.g. the map n->2n).

We can take an even "sparser" subset of the natural numbers: the prime numbers. This subset of the natural numbers also has the same size, aleph_0 (e.g. the map n->n-th prime number).

My question is: is there an "sparsest" subset of the natural numbers, such that if we take out any infinitely sized subset of it, it is not aleph_0 anymore?