Tao

1. Ex 5.4.3,
2. 5.4.5 (you may assume result in 5.4.4)
3. 5.4.7,
4. 5.4.8
5. Let $A$ be the subset of $\Q$ consisting of rational numbers with denominators of the form $2^m$. Prove that for any $x \in \R$, there is a Cauchy sequence $(a_n)$ in $A$, such that $x = \LIM a_n$.