*melinda*
- 86
- 0
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.
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.