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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.

Siong Thye Goh
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Minnow
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    ${1,...,5} $ works, but I don't believe there is a single symbol to denote the range. – Dave Dec 13 '16 at 04:46
  • 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 05:24
  • 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. – LudvigH Jul 21 '22 at 08:29

3 Answers3

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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 $b$. ($[1\ldotp\ldotp 5] = \{1,2,3,4,5\}$)

Henricus V.
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    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. – Nenunathel Oct 27 '20 at 11:49
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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

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

Graham Kemp
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Hypergeometricx
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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 $$\{\frac{1}{2} k \mid k \in [-6..6] \}.$$

Emil Jansson
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