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Simple set notation

  1. Jul 13, 2005 #1
    *Suppose I want to find the range of the set [tex] \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} [/tex], that is, the difference between the maximum and minimum values (of the elements that is!) in the set.

    Do I have to fully write out,
    [tex] \max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} [/tex]

    Or is there some nice shorthand/other notation to use ?
    Maybe something like
    [tex] \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}|_{\min }^{\max } [/tex] ??

    *Is there any symbol/notation/shorthand available to represent a set's range?
    (b/c writing out [itex] \max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} [/itex] is quite tedious:redface:!!)
     
  2. jcsd
  3. Jul 13, 2005 #2
  4. Jul 13, 2005 #3
    I know what range means, mr. iNCREDiBLE ...
    (that's not the problem)

    I just need a better notation for it!

    From reading those pages, I suppose the notation would be
    [tex] {R} \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} [/tex] ?

    Am I correct ?
     
    Last edited: Jul 13, 2005
  5. Jul 13, 2005 #4
    I know that you know what it means, mr. bomba923. I'm just trying to help you.
    It says clearly that the range is denoted as [tex]R = max_j(t_j) - min_j(t_j)[/tex].
     
  6. Jul 13, 2005 #5
    Which pretty much is the same as..
    Except for the subscripts identifying which variable is considered for maximums/minimums and that the sets are written in condensed form :cool:
     
  7. Jul 14, 2005 #6

    EnumaElish

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    Using "order stats" notation, you could write t(n:n) - t(1:n), could even write t(n) - t(1). Or you could type "XYZ" for range and then do a search-and-replace with the correct notation.
     
  8. Jul 14, 2005 #7
    Hey, um, just one more notation question:
    *Is it generally understood that [tex] \mathbb{Q}^ + [/tex] refers to the set of all positive rationals?
    (just like [itex] \mathbb{R}^ + [/itex] refers to the set of all positive reals)

    Right?
     
  9. Jul 15, 2005 #8

    EnumaElish

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    I am not a mathematician by trade, but I have seen both R+ and R+ to refer to positive reals; so by extrapolation I guess same notation would hold for Q as well.
     
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