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Math Help - increasing sequence

  1. #1
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    increasing sequence

    Let A be a subset of R that is bounded above and let  u= sup A . Prove that there is an increasing sequence  a_n with a_n \in A , \forall \ n \in N SUCH THAT  a_n \to u
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    Quote Originally Posted by flower3 View Post
    Let A be a subset of R that is bounded above and let  u= sup A . Prove that there is an increasing sequence  a_n with a_n \in A , \forall \ n \in N SUCH THAT  a_n \to u
    As written that is a false statement.
    Let A=[0,1]\cup\{2\}.

    It is true if we know that u \notin A.
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