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

Interval Notation - dCode

Tag(s) : Mathematics

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*!

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

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)

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 $)

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) $

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, copy-paste, or API access will be for free, same for Interval Notation download for offline use on PC, tablet, iPhone or Android !

Please, check our community Discord for help requests!

interval,inequality,set,number,bracket

Source : https://www.dcode.fr/interval-notation

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲