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Homework Help: Proof or counterexaample of Floor 7 Ceiling

  1. Mar 29, 2010 #1
    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. jcsd
  3. Mar 29, 2010 #2


    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.
  4. Mar 29, 2010 #3


    User Avatar
    Homework Helper

    Is your first question whether the following statement is true or false?

    \text{ceiling}(x \times y) = \text{ceiling}(x) \times \text{ceiling}(y)

    If so - try a few test values for [itex] x [/itex] and [itex] y [/itex].
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