Simple set notation

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  • #1
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Main Question or Discussion Point

*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:!!)
 

Answers and Replies

  • #3
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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 ?
 
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  • #4
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bomba923 said:
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 ?
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].
 
  • #5
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iNCREDiBLE said:
It says clearly that the range is denoted as [tex]R = max_j(t_j) - min_j(t_j)[/tex].
Which pretty much is the same as..
bomba923 said:
[tex] \max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} [/tex]
Except for the subscripts identifying which variable is considered for maximums/minimums and that the sets are written in condensed form :cool:
 
  • #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.
 
  • #7
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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?
 
  • #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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