Finding Range of Set: Notation & Shorthand

[bomba923]

*Suppose I want to find the range of the set $$\left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$, 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,
$$\max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$

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

*Is there any symbol/notation/shorthand available to represent a set's range?
(b/c writing out $\max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$ is quite tedious!)

 

[iNCREDiBLE]

Check http://mathworld.wolfram.com/OrderStatistic.html and http://mathworld.wolfram.com/StatisticalRange.html

 

[bomba923]

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
$${R} \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$ ?

Am I correct ?

 

[iNCREDiBLE]

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
$${R} \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$ ?

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 $$R = max_j(t_j) - min_j(t_j)$$.

 

[bomba923]

It says clearly that the range is denoted as $$R = max_j(t_j) - min_j(t_j)$$.

Which pretty much is the same as..

$$\max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$

Except for the subscripts identifying which variable is considered for maximums/minimums and that the sets are written in condensed form

 

[EnumaElish]

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.

 

[bomba923]

Hey, um, just one more notation question:
*Is it generally understood that $$\mathbb{Q}^ +$$ refers to the set of all positive rationals?
(just like $\mathbb{R}^ +$ refers to the set of all positive reals)

Right?

 

[EnumaElish]

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.