This problem considers the bijection h : N $->$ N $\backslash$times N that was discussed in

class. Important in the proof were the squares S$(0),$ S$(1),$ S$(2),...$ defined by

S$($m$)=\{($x$,$ y$)$ in N $\backslash$times N $|0<=$ x $<=$ m and $0<=$ y $<=$ m$\}$

$($a$)$ How many gridpoints are in square S$($m$)?$

$($b$)$ Given any m in N$,$ what is the maximum n such that h$($n$)$ in S$($m$)?$

$($c$)$ Given any m in N$,$ with m $>=1,$ what is the minimum n such that h$($n$)$ in S$($m$)$

S$($m $1)?$

$($d$)$ What is h$1($m$,$ m$)?$

$($e$)$ What is h$1(100,200)?$

$($f $)$ What is h$1(300,200)?$