My class is starting to discuss topics in analysis. I really need some help with

Question

My class is starting to discuss topics in analysis. I really need some help with these two problems:

Prob. 1: Consider A = [2, 4). Show that 5 is an upper bound but not a least upper bound for A. Prove that 2.1 is not a lower bound for A and that 4 is the least upper bound for A.

Prob. 2: Show that 5 is an upper bound but not a least upper bound for the set S = { x is a member of R | there exists a natural number n such that x = 1 - (1/n). Find its least upper bound.

I'd appreciate anyone's help in explaining these two problems. I'll quickly give the points to the best answer. Thanks!

Explanation / Answer

1. The values that A can take are:

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