What ⌈ means
It opens a ceiling expression that rounds up. ⌈x⌉ means the smallest integer greater than or equal to x: ⌈2.1⌉ is 3, ⌈−2.1⌉ is −2, and ⌈4⌉ stays 4.
Writers use it when a count must cover everything: ⌈n/2⌉ pages, servers or rounds, never a fraction. It is the bracket form of the ceil() function found in programming languages.
Who invented the ceiling bracket?
Kenneth Iverson, in 1962. Iverson, creator of the APL programming language, named floor and ceiling and drew them as square brackets missing one horizontal stroke. Earlier, Legendre used an integer-part notation in 1798 and Gauss wrote square brackets for rounding down in 1808, with no matching mark for rounding up.
In APL, ⌈ works alone: ⌈2.1 gives 3, and 3⌈7 gives the larger value, 7.
How do I type the ceiling bracket in a formula?
Write \lceil and \rceil in LaTeX or MathJax. Around a tall fraction, \left\lceil … \right\rceil stretches both halves to fit; the plain character never stretches. Outside formula tools, enter it by its code point, 2308.
Technical and formal: maths papers, algorithm write-ups, code documentation.
In ordinary maths, ⌈ without a closing ⌉ reads as a typo.
Don't confuse it with
3Combination ideas
3Questions people ask
1Why does left ceiling look different in LaTeX?
It can grow. With \left and \right the bracket stretches around a fraction, and LaTeX math fonts draw it differently from text fonts; the literal character stays one fixed glyph.
How to type ⌈
⌈\2308Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.