For a real number x, find the number of different possible values of \(\lfloor x \rfloor + \lfloor -x \rfloor\).
I actually have no clue how to start this one, except just try values.
+128408 We have two cases
Let x be positive and - x be negative
If x is an integer then floor (x) = x and floor (-x) = -x
So x + - x = 0
If x is NOT an integer, then floor (x) = a where a is a positive integer and floor (-x) = -a - 1
So a + ( - a - 1) = -1
So.....all possible values of the sum of the floor functions = - 1 , 0
