MAT511 homework,         due Nov 19, 2003

1. Prove that the two intervals $(0,1)$ and $(-47,47)$ have the same cardinality.

2. Prove that if $A$ is an infinite set and $A \subseteq B$, then $B$ is an infinite set.

3. Let $3{\mathbb{N}}$ be the set of naturals that are multiples of 3, that is $3{\mathbb{N}}= \left\{{ 3, 6, 9, 12 \ldots}\right\}$. Prove that ${\mathbb{N}}- 3{\mathbb{N}}$ is a countably infinite set.