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Math Help - Proving countable set

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    Proving countable set

    I need help proving that the set: (1/2, 2/3, 3/4,...,n/n+1,...) is countable.
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    Quote Originally Posted by redwings6 View Post
    I need help proving that the set: (1/2, 2/3, 3/4,...,n/n+1,...) is countable.
    Let G = \left\{ {\frac{n}{{n + 1}}:n \in \mathbb{Z}^ +  } \right\}.
    Now define \Phi:G\mapsto \mathbb{N} by \Phi \left( {\frac{n}{{n + 1}}} \right) = n.

    Prove that \Phi is injective.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by redwings6 View Post
    I need help proving that the set: (1/2, 2/3, 3/4,...,n/n+1,...) is countable.
    Alternatively, clearly \eta:\mathbb{N}\to K:n\mapsto\frac{n}{n+1} is an overkill surjection.

    Clearly Plato's answer along with "every infinite subset of a countable set is countable" is better though.
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