Hello, I am new here and was wondering if anyone can help me with this problem:

Prove that the greatest integer function has the following properties

A) [x+n]= [x]+n for every integer n.

B)

[-x]= -[x] if x is an integer

-[x]-1 otherwise.

The integer n is called the greatest integer of x and is denoted by [x].

Thank you, in advance