Mathematicians, engineers, and physicists enjoy defining functions to make their lives

easier $($or harder sometimes $...).$ Some of these function are here to stay. One

is the floor$($x$),$ also denoted by $$x$,$ takes the argument x and returns the largest

integer less than or equal to x$.$ Thus $2\mathrm{.}1=2,\backslash$pi $=3,0\mathrm{.}1=1,$and $1=1.$

$($a$)$ Plot this $$funny$$ function using SageMath. At what point$($s$)$ is $$x$$ discontinuous?

$($b$)$ Identify real$-$world scenarios $$x$$ might be useful. Be as specific as possible.