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Upper bounds of a given set

  1. Mar 17, 2012 #1
    #Upper bounds of a given set

    In my analysis book it says:
    "If a set has a upper bound, there are infinitely many upper bounds".
    Why is this correct? If you have some finite set, won't there be just one?
     
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  3. Mar 17, 2012 #2

    HallsofIvy

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    Re: #Upper bounds of a given set

    If a is an upper bound, what about a+1, a+ 2, a+ 3, ...? Are you clear on what an "upper bound" is?
     
  4. Mar 17, 2012 #3
    Re: #Upper bounds of a given set

    Ah yes of course, I misread the definition.
     
  5. Mar 17, 2012 #4

    HallsofIvy

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    Re: #Upper bounds of a given set

    Note, that if you are talking about sets of real numbers, if a set has any upper bounds, then it has a unique least upper bound.
     
  6. Mar 17, 2012 #5
    Re: #Upper bounds of a given set

    And that unique least upper bound is called supreme.

    If the supreme belongs to the set, then it's called a maximum.

    EDIT: I need confirmation on the terms "supreme" and "maximum" since I've learnt Analysis in spanish and translations might not be accurate
     
  7. Mar 17, 2012 #6

    Office_Shredder

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    Re: #Upper bounds of a given set

    In english it's typically called the supremum
     
  8. Mar 18, 2012 #7

    HallsofIvy

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    Re: #Upper bounds of a given set

    Which is actually Latin!!
     
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