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Thread: Denumerability of a subset of a denumerable subset

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    Denumerability of a subset of a denumerable subset

    The following is an excerpt from Serge Lang's "Real and Functional Analysis"
    Denumerability of a subset of a denumerable subset-lang.png

    In the proof, the author defines $\displaystyle \left \{k...k_n \right \}$ as a subset of $\displaystyle D$.

    How does he know that $\displaystyle D$ is big enough to contain a set of elements that can be indexed to $\displaystyle n$?

    I assume that, by $\displaystyle n$, the textbook means an index set with the same cardinality as the natural numbers.
    Last edited by Schiavo; Sep 26th 2015 at 08:44 PM.
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