# Simple set notation

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
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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 ?

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

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
iNCREDiBLE said:
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..
bomba923 said:
$$\max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\}$$
Except for the subscripts identifying which variable is considered for maximums/minimums and that the sets are written in condensed form

Homework Helper
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?