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Domain and image of a function

  1. Sep 7, 2008 #1
    We recall that Z is the set of all integers. For each i, j in Z, let f(i,j) be the larger of the two integers i and j. Do these remarks define a function? If so, what are the domain and the image?

    I'm not sure how to do this. I believe that the remarks do define the function. But I don't know about the domain and image. Wouldn't the domain have to be bigger than the image making it Z^2 and the image Z?

    Is this right?

    Thanks for the help!
     
  2. jcsd
  3. Sep 7, 2008 #2

    Dick

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    The domain is Z^2 and the image is Z. That's correct. But can you give better reasons?
     
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