$)$ Let S R$.$ Show that x $2$ S i$$

inf fjx sj j s $2$ Sg $=0$:

Please follow steps:

$(2$ pts$)$ Let x $2$ S and let $>0.$ Explain why for $>0$;

D $($x; $)\backslash$ S $6=$ ;:

$(3$ pts$)$ Take s $2$ D $($x; $)\backslash$ S and explain why

$0$ inf fjx sj j s $2$ Sg