Comment by thom

Because everyone gave me such good and well meaning answers perhaps you’ll permit me a follow up.

As I understand it we can say the cardinality of the reals is 2^aleph_0. Why is it cheating to create a bijection thusly:

    0 -> 0
    1 -> 1/(2^aleph_0)
    2 -> 2/(2^aleph_0)

etc?