# Prove lim = inf(x)

1. Sep 19, 2005

### *melinda*

Question:

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

I am not sure but it seems like my $x=lim(x_n) =liminf(x_n)$.
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.