Explore BrainMass

Explore BrainMass

    Cartesian product proof

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    I need help constructing a proof for the
    Cartesian product of finitely many countable sets is countable.

    © BrainMass Inc. brainmass.com March 6, 2023, 1:17 pm ad1c9bdddf

    Solution Preview

    First let's state the counting theorem:
    "The Counting Theorem":
    Let S be a set. The following are equivalent.
    (i) S is either finite or a countably infinite set.
    (ii) Either S = Null or there is a surjective map alpha: N ---> S.
    (iii) There is an injective map beta: S ---> N.
    If any of these three equivalent conditions hold, then we say
    that S is a countable set.
    This theorem has a ...

    Solution Summary

    This is a proof regarding the Cartesian product of countable sets.