1. Limited time only! Sign up for a free 30min personal 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!

Proof abstract

  1. Aug 30, 2009 #1
    1. The problem statement, all variables and given/known data
    For each ordered pair ( a, b) of integers define a mapping alpha (a, b) : Z into Z by alpha (a, b)( n) = an + b.
    ( a) For which pairs ( a, b) is alpha a, b onto?
    ( b) For which pairs ( a, b) is alpha a, b one- to- one?


    2. Relevant equations



    3. The attempt at a solution
    To solve this question do i just solve by using a counter example with using any integers or
     
  2. jcsd
  3. Aug 30, 2009 #2
    Find and b if alpha is onto:

    Let c be an arbitrary integer. Since alpha is onto then there must exist some integer n so that an + b = c. Knowing that c and n are integers, find appropriate a and b.

    Find a and b if alpha is one-to-one:

    Let m and n be integers so that an + b = am + b. Find a and b so that this implies that m = n.

    Note that multiple values for a and b may exist for either problem.

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




Similar Discussions: Proof abstract
  1. Abstract Proof (Replies: 6)

Loading...