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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.

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# Homework Help: Prove lim = inf(x)

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