Finding Range of Set: Notation & Shorthand

In summary, there are multiple notations for representing the range of a set, including using the "order stats" notation of t(n:n) - t(1:n) or t(n) - t(1), or using the symbol "R" to represent the range in the form R = max_j(t_j) - min_j(t_j). It is also generally understood that \mathbb{Q}^+ refers to the set of all positive rationals.
  • #1
bomba923
763
0
*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:!)
 
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  • #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 ?
 
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  • #4
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
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
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
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
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.
 

1. What is the notation used for finding the range of a set?

The notation used for finding the range of a set is called set builder notation. It is written in the form of {x | P(x)}, where x represents the elements in the set and P(x) is the condition or rule that the elements must satisfy.

2. How is set builder notation different from interval notation?

Set builder notation is used to describe individual elements within a set, while interval notation is used to describe a continuous range or interval of values. Interval notation uses brackets or parentheses to indicate whether the endpoints are included or excluded.

3. What is meant by "shorthand" notation for finding the range of a set?

Shorthand notation for finding the range of a set is a simpler and more concise way of representing the set. It usually involves using symbols such as "∈" to indicate membership in a set, or "∪" to represent the union of two sets.

4. How can I determine the range of a set from a graph?

To determine the range of a set from a graph, you can look at the vertical axis (y-axis) and identify the highest and lowest points on the graph. The range will be the set of all y-values between these two points, including the endpoints if they are included.

5. What is the importance of finding the range of a set in mathematics?

Finding the range of a set is important in mathematics as it helps us understand the spread or variability of a data set. It also allows us to identify the maximum and minimum values in a set, which can be useful in solving equations and inequalities.

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