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Math Help - Order Relations, immediate sucessors and predecessors

  1. #1
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    Order Relations, immediate sucessors and predecessors

    We have an order relation of Z+ x Z+ (where Z+ denotes the positive integers.)
    (a,b) < (c,d) if either a - b < c -d or a -b = c - and b < d
    is an order relation

    (a) which elements have immediate predecessors?
    (b) which elements have immediate successors?
    (c) Does the set Z+ x Z+ have a smallest element?

    Can someone help I am really lost of this one.
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  2. #2
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    either a - b < c -d or a -b = c - and b < d
    Something unclear about "= c -". Is it supposed to be "= c - d" or is "-" just a syntactic long dash?

    In general, I would take a graph paper and draw some arrow from smaller points to greater. I need some intuition to figure this out.
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