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Set of paired elements

  1. Nov 27, 2007 #1
    Hi all,

    I'm trying to express a given requirement in a software system. I'm used to UML and UseCase specification, but I thought I would attempt to learn Zed Specification (which is based off logic, set theory., etc... so those topics too!)

    Given two sets of data
    e.g. in Zed notation

    [X] ::= a|b|c|d
    [Y]::= 1|2|3|4

    or in Set Theory

    X = {a,b,c,d}
    Y = {1,2,3,4}

    In set notation I am having difficulty trying to write down the formula for specifying a set containing a list of pairs made from X and Y. Note: Not a Cartesian Product.
    So I'm looking for a Set definition for something like this:

    MysterySet = {(a,1),(b,2),(c,3),(d,4)}
    or a further example,
    Material = {(chair,wood),(table,metal),(cup,clay)}

    This is basically an analogy for a key-value pair.

    Thanks very much.
     
  2. jcsd
  3. Nov 27, 2007 #2

    Hurkyl

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    I can't decipher just what it is you are trying to do...
     
  4. Nov 27, 2007 #3
    Hi :smile:

    I'm just trying to write a set definition for a set containing a list of paired values. Where each paired value is a single member of that set.

    For example the set of all married couples Married = {(bob,jane),(fred,susan),(mike,sarah)} will have been built from the two sets: female={jane,susan,sarah} and male={bob,fred,mike}

    So in a set definition how do I say something like:

    each element in the set "Married" is a paired value from an enumerated one-to-one mapping between an element in the set male to the set female.

    Hope that help! :biggrin: I could do this is a second programmatically but I have become extremely interested in modeling using set theory and logic, although it's something I've only just strated learning.

    Thanks
     
  5. Nov 28, 2007 #4
    After having done further research, it looks like a set of key-valued pairs might be (might be, being this is what I have thought up myself) represented as the set of all bijections as denoted X[tex]\leftrightarrow[/tex]Y.

    So would I be right in saying (this is so sketchy and grasping at straws)
    If I have a dom X = {1,2,3} and ran Y = {a,b,c} then a set S = {f:X[tex]\leftrightarrow[/tex]Y} would infact look like S={(a,1),(b,2),(c,3)}

    P.S. Still getting used to the Latex function on this forum :rolleyes:

    Thanks
     
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