# 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
Commented Dec 13, 2016 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. Commented Dec 13, 2016 at 5:24
• An finite ordered set of $n$ elements is called a $n$-tuple, and is commonly denoted with parenthesis, e.g. $(1,2,...,5)$ for the 5-tuple of 1 to 5. But this notation clashes with open intervals, when working with 2-tuples. So you should probably add some explanatory text depending on who your target audience is. Commented Jul 21, 2022 at 8:29

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. Commented Oct 27, 2020 at 11:49

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)? Commented Apr 28, 2020 at 17:31
• @MadPhysicist absolutely Commented Nov 15, 2020 at 2:27

I would like to add to Henricus answer as it gives the answer for a integer range but not for ranges of general step sizes, which is something that is very common in programming.

The expression

$$\{s k \mid k \in [a..b] \}$$ would give you a range from $$sa$$ to $$sb$$ with increments of s.

So if you wanted to write an expression for the numbers $$\{-3,-2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3\}$$ that could be written as $$\{\frac{1}{2} k \mid k \in [-6..6] \}.$$