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*!

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 "Interval Notation" source code. Except explicit open source licence (indicated Creative Commons / free), the "Interval Notation" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Interval Notation" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Interval Notation" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Interval Notation" or any of its results, is allowed (even for commercial purposes) as long as you cite dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Interval Notation* on dCode.fr [online website], retrieved on 2023-09-21,

interval,inequality,set,number,bracket

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

© 2023 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback