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.