We are given an infinite set of rectangles in the plane, where each rectangle has vertices of the form $(0,0), (n,0), (0,m) (n,m)$ for positive integers $m$ and $n$ ($m$ and $n$ vary from rectangle to rectangle).
(a) Prove that there exist two rectangles in the set such that one contains the other.
(b) * Prove or disprove: there must exist an infinite sequence $R_1,R_2,\ldots,R_n,\ldots$ of rectangles in the set such that $R_1$ is contained in $R_2$, $R_2$ is contained in $R_3$, and so on. ($R_i$ is contained in $R_{i+1}$ for each $i$).