Search for a tool
Interval Notation

Tool to convert to write intervals into inequalities and vice versa. Intervals/Ranges notation represent sets of numbers between two values.

Results

Interval Notation -

Tag(s) : Mathematics

Share dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our community Discord for help requests!

Thanks to your feedback and relevant comments, dCode has developped the best 'Interval Notation' tool, so feel free to write! Thank you !

# Interval Notation

## Inequality to Interval Converter

 Locale Notation European ]…;…[ American (…;…)

## Set Notation Converter

 Convert to Inequality … < … Interval notation […;…] (only one)
 Locale Notation European ]…;…[ American (…;…)

Tool to convert to write intervals into inequalities and vice versa. Intervals/Ranges notation represent sets of numbers between two values.

### What is an interval? (Definition

An interval is a notation which makes it possible to define a set of real numbers included between a lower limit (minimum admissible value) and an upper limit (maximum admissible value).

There are 3 types of intervals (taking ${a, b} \in \mathbb {R}$ with $a < b$) and a variable $x \in \mathbb {R}$:

- open interval (or unclosed interval)

Example: $a < x < b = ] a; b [$

- closed interval (or unopened interval)

Example: $a \leq x \leq b = [a, b]$

- half-open (or half-closed) interval

Example: $a < x \leq b = ] a, b ]$ (half-open interval on the left or half-closed interval on the right)

Example: $a \leq x < b = [ a, b [$ (half-closed interval on the left or half-open interval on the right)

### How to convert an interval into an inequation?

Here is the list of different types of intervals and the corresponding inequalities:

$] a ; b [ \iff a < x < b \quad$ (or $b > x > a$)

$[ a ; b [ \iff a \leq x < b \quad$ (or $b > x \geq a$)

$] a ; b ] \iff a < x \leq b \quad$ (or $b \geq x > a$)

$[ a ; b ] \iff a \leq x \leq b \quad$ (or $b \geq x \geq a$)

A shorter writing of the inequality is possible if $a$ or $b$ has for value $\infty$

$] -\infty ; b [ \iff x < b \quad$ (or $b > x$)

$] -\infty ; b ] \iff x \leq b \quad$ (or $b \geq x$)

$] a ; +\infty [ \iff x > a \quad$ (or $a < x$)

$[ a ; +\infty [ \iff x \geq a \quad$ (or $a \leq x$)

### What is the European notation and the American notation?

There are two schools, two ways of writing which differ in the notation of open intervals.

European notation, which uses square brackets everywhere and denotes open intervals with an outward bracket: $[a; b [$

American notation, which uses either square brackets for closed intervals and denotes open intervals with a parenthesis: $[a; b)$

## Source code

dCode retains ownership of the online 'Interval Notation' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Interval Notation download for offline use on PC, tablet, iPhone or Android !

## Need Help ?

Please, check our community Discord for help requests!