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Describing partition

  1. Mar 30, 2008 #1
    1. The problem statement, all variables and given/known data
    a. Let A={1,2,....10}. Describe a partition of A that gives rise to five distinct paritioning sets.
    b.Describe a partition of Z that gives rise to five distinct partitioning sets
    c. Describe a partition of R that gives rise to five distint partitioning sets



    2. Relevant equations



    3. The attempt at a solution

    Could someone please explain to me how to describe a partion in general? Is this where you say that each level has a certain amount of multiples of the set?

    Thank you very much
     
  2. jcsd
  3. Mar 31, 2008 #2

    HallsofIvy

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    You "describe" a partition by telling what sets are in it! Are you clear on what a partition is? It is simply a collection of subsets of the original set such that each member of the original set is in one and only one of the subsets.

    For example, if I were asked to find a partition of {1, 2, 3, 4, 5, 6, 7} consisting of "5 distinct sets" I might give {{1}, {2}, {3}, {4}, {5, 6, 7}}. That's a partition (each member of the set is in exactly one of those) and it has 5 distinct sets. That's all that's required.

    Now, for "b.Describe a partition of Z that gives rise to five distinct partitioning sets", yes, one way to do that is to use "modulo 5"- each set containing all integers whose remainder, when divided by 5, is the same. Another perfectly valid answer, since it is not required that each set in a partition be the same size, would be {{all negative integers},{1},{2},{3}, {all integers larger than 3}}.
     
  4. Mar 31, 2008 #3
    Thank you very much

    Part c. "Describe a partition of R that gives rise to fie distinct partitioning sets" could be the same thing as part b., right? For these types of problems, there isn't just one correct answer, right?

    Thank you
     
  5. Mar 31, 2008 #4

    HallsofIvy

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    No, (c) is not the same as (b). (b) asked for a partition of Z, the set of integers, so the partition must include only sets of integers. (c) is asking for a partition of R, the set of real numbers, so the partition must include all real numbers.
     
  6. Mar 31, 2008 #5
    Thank you very much

    Regards
     
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