help please see below

Question

anonymous · Answer

the set of integers as $$\mathbb{Z}^- {....-3,-2,-1,0,1,2,3....}$$
the greatest integer of x is denoted as 
$$\lfloor x \rfloor$$
is defined to be the largest interger k with $$k \le x$$
discuss with your classmates how $$\lfloor x \rfloor$$ may be described as a piecewise defined function

anonymous · Answer

also is 
$$\lfloor a+b \rfloor = \lfloor a \rfloor+\lfloor b \rfloor$$
always true? what if a or b was an integer? test some values make a conjecture and explain your result

anonymous · Answer

@DebbieG  or @Directrix

debbieg · Answer

You'll gain a better understanding of this function if you look at some of the values of it.

$\lfloor 3 \rfloor=3$     
$\lfloor 3.2 \rfloor=3$   
$\lfloor 3.8 \rfloor=3$   
$\lfloor 3.9999 \rfloor=3$
$\lfloor 4 \rfloor=4$  

So, for example

$\lfloor x \rfloor=3$  for  $3\le x <4$    

Now think about extending that idea over the whole set of integers, and you should see this as a piecewise function.

For the 2nd question, try some values and see if $\lfloor a+b \rfloor = \lfloor a \rfloor+\lfloor b \rfloor$. E.g., compare

$\lfloor 4 \rfloor+\lfloor 5 \rfloor$  to $\lfloor 4+5 \rfloor$ 

$\lfloor 4.9 \rfloor+\lfloor 5.9 \rfloor$  to $\lfloor 4.9+5.9 \rfloor$