Problem:
Investigate graphically the behavior of the function

for values of x near 2. [[ x ]] denotes the greatest integer less than or equal to x.

Visualization:
Using Maple:

Maple uses the command floor for the greatest integer function.

> plot(floor(x),x=-2..5,discont=true,color=blue);

> limit(floor(x),x=1);

undefined

> limit(floor(x),x=1,right);

1

> limit(floor(x),x=1,left);

0

> g:=x->floor(x)+floor(-x);

> g(2);

0

> limit(g(x),x=2);

1

> plot(g(x),x=-2..5);