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Thread: E subset N

  1. #1
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    E subset N

    Let E$\displaystyle \subset$N a infinite subset. Show that exist a$\displaystyle \in$R such that {floor(a^k); k $\displaystyle \in$N}$\displaystyle \cap$E, contains infinites integers.

    I try this:
    floor(a^k) =n$\displaystyle \in$E$\displaystyle \Longleftrightarrow$k log a$\displaystyle \in$(log n, log n+1) and ?????nothing
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  2. #2
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    Nested intervals????
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