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Homework Help: Determining whether floor((n+1)/2) is 1-to-1 or onto

  1. Dec 13, 2015 #1
    1. The problem statement, all variables and given/known data

    floor((n+1)/2)

    Find whether this function is 1-to-1 and/or onto from Z to Z.

    2. Relevant equations


    3. The attempt at a solution

    This is not one-to-one because f(1) = f(2) = 1.

    Regarding onto, we need to show that f(a) = b

    floor((n+1)/2) = b
    2b = n + 1
    n = 2b - 1

    f(2b-1) = floor((2b-1) + 1)/2) =

    floor(2b/2) = floor(b) = b.

    I'm not sure how to take the floor function into account for my onto calculations.





     
  2. jcsd
  3. Dec 13, 2015 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    Let f be the function defined by f(n)=floor((n+1)/2) (n∈ℤ).

    I may be confused, but haven't you actually proved that for b∈ℤ, f(2b-1)=b?
    That proves that f in onto.
     
  4. Dec 13, 2015 #3

    Mark44

    Staff: Mentor

    In more detail, you need to show that for each ##b \in Z##, there exists an ##a \in Z## such that f(a) = b.
     
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