# What is the mathematical symbol for range?

An unsophisticated question from a neophyte:

Given the numbers: $1,2,3,4,5$

What is the symbol for the range of the numbers?

i.e. the lowest-highest number in the set. For example, the min max is $1-5$.

The ____ is $1-5$. (insert math symbol into blank).

Should such a beast exist, I'd be particularly interested in it's unicode character...

Tried searching a few online resources, such as: http://rapidtables.com/math/symbols/Basic_Math_Symbols.htm without success.

• $\{1,...,5\}$ works, but I don't believe there is a single symbol to denote the range. – Dave Dec 13 '16 at 4:46
• I think that both of the current answers miss the heart of the question. It seems like OP is looking for a notation that means "the smallest interval containing a given subset $S \in \mathbb R$", or similar thereto. – Erick Wong Dec 13 '16 at 5:24

You are looking for either:

1. A closed interval: $[a,b]$ represents the set of all real numbers greater or equal to $a$ and less or equal to $b$.

2. A integer interval: $[a\ldotp\ldotp b]$ represents all integers in between $a$ and $b$. ($[1\ldotp\ldotp 5] = \{1,2,3,4,5\}$)

• This however are just "unordered" sets. What if I want to represent a list of numbers that go from 1 to 5? Conventionally that is written 1-5, which can be confused with a minus. In programming you use 1:5, which can be confused with the "such that" symbol in math. I don't know of other signs that might be less confusing than these two. – user3604362 yesterday

This is a useful wikipedia reference.

It is important to make the distinction between whether or not a particular endpoint is included. Use ( or ) to exclude and [ or ] to include.

For instance

$$(a,b) \;\;\Rightarrow \;\; \{x\in\Bbb R:a<x<b\}$$ $$[a,b] \;\;\Rightarrow \;\;\{x\in\Bbb R:a\le x\le b\}$$ $$\{a..b\} \;\;\Rightarrow \;\;\{x\in\Bbb Z:a\le x\le b\}$$

• Does that mean that I can write something like $\varphi\in[0,\pi]$ (and be generally understood)? – Mad Physicist Apr 28 at 17:31