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Math Help - Set of all counting numbers

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    Set of all counting numbers

    Prove: The set of all counting numbers is infinite.
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    Quote Originally Posted by noles2188 View Post
    Prove: The set of all counting numbers is infinite.
    It is clear that f:\mathbb{N} \mapsto \mathbb{N}\;,\,f(n) = 2n is an injection to a proper subset.
    That is sufficient to prove a set is infinite.

    However, I think you are working in a more structured setting.
    So that should be a lesson to you.
    Completely explain the setting of your question.
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  3. #3
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    Ok, here is the setting:
    The statement that the set A is infinite means that there is a nonempty proper subset B of A such that there is a one-to-one correspondence between A and B. By a counting number means a number in the minimal induction set, and the minimal induction set is called the set of all counting numbers and is denoted by C.
    Hopefully this helps; I'm not good at starting these proofs, so any help is much appreciated.
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