# Finding Range of Set: Notation & Shorthand

• bomba923
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.
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!)

Last edited by a moderator:
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 ?

Last edited:
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 $$R = max_j(t_j) - min_j(t_j)$$.

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

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.

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?

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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