Question 1
Which statement is the least upper bound property that characterizes completeness of $\mathbb{R}$?
Question 2
What does the completeness of $\mathbb{R}$ imply about a Cauchy sequence $(a_n)$ in $\mathbb{R}$?
Question 3
Why is $\mathbb{Q}$ not complete?
Question 4
What is $\sup\{x\in\mathbb{R}: x^2<2\}$?
Question 5
If $(a_n)$ is increasing and bounded above in $\mathbb{R}$, what must happen?
