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Notation Question

  1. Apr 17, 2005 #1
    Let's say I have a set {A}. How do I denote the largest member of that set?
    For example, let's say I have a solution set of discrete values. How do I denote the largest solution?

    Basically, with any set, how do I denote the largest member of that set? What symbol/s do I use !?
     
  2. jcsd
  3. Apr 17, 2005 #2

    arildno

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    What's wrong with something like [tex]max(A)[/tex]??
     
  4. Apr 17, 2005 #3
    That is the formal/accepted way of expressing it (the largest member of a set), right?
     
  5. Apr 17, 2005 #4

    honestrosewater

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    Do maximums differ from least upper bounds (supremums)? The definitions I found didn't clear this up. Edit: Eh, because I was going to say supremum.
     
  6. Apr 17, 2005 #5
    AFAIK, the maximum of a set must necessarily be a member of the set as well. So for example, {1 - 1/n; n a natural} has a supremum, but no maximum.
     
  7. Apr 17, 2005 #6

    matt grime

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    Muzza is absolutely correct.

    given a set (presumably of real numbers) there is no reason for that set to even have a greatest element, even if it is bounded above (ie all elements are less than some constant K). The sup is the smallest such K that bounds them above, and this is the max if and only if K is an element of the set.

    Note, that this only applies to infinite sets. Any finite set of points must have a maxmimum.
     
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