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Homework Help: 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.

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