# Proof or counterexaample of Floor 7 Ceiling

1. Mar 29, 2010

### nastygoalie89

1. The problem statement, all variables and given/known data

For all real numbers x and y, ceiling of x,y = ceiling of x times ceiling of y
For all odd integers n, ceiling of n/2 = (n+1)/2

2. Relevant equations

definition floor: floor of x = n n<or equal to x < n+1
definition ceiling: ceiling of x=n n-1 < x <orequal to n.

3. The attempt at a solution

No idea where to even start. I don'r quite understand the concept and floor & ceiling.

2. Mar 29, 2010

### Staff: Mentor

I don't understand what you are asking in the problem above. What does "ceiling of x, y" mean?
This one is straightforward. If n is odd, then n/2 will have a fractional part that is 1/2 or .5.
Your definitions are not precise enough to be helpful. floor(x) is the largest integer that is less than or equal to x. For example, floor(2) = 2, and floor (1.99) = 1

ceiling(x) is the smallest integer that is greater than or equal to x. For example, ceiling(5) = 5, and ceiling(1.01) = 2.

3. Mar 29, 2010

$$\text{ceiling}(x \times y) = \text{ceiling}(x) \times \text{ceiling}(y)$$
If so - try a few test values for $x$ and $y$.