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Prove lim = inf(x)

  1. Sep 19, 2005 #1
    Question:

    Suppose there is a set [itex]E\subset \Re[/itex] is bounded from below.
    Let [itex]x=inf(E)[/itex]
    Prove there exists a sequence [itex]x_1, x_2,... \in E[/itex], such that [itex]x=lim(x_n)[/itex].

    I am not sure but it seems like my [itex]x=lim(x_n) =liminf(x_n)[/itex].
    In class we constructed a Cauchy sequence by bisection to find sup. To do this proof I was thinking that I should do the same, but do it to find inf.

    Does this seem like it will work?
    Any suggestions would be greatly appreciated.
    Thanks.
     
  2. jcsd
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