1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Determining whether floor((n+1)/2) is 1-to-1 or onto
  1. Functions: 1-1, onto (Replies: 6)

Loading...