# Types of Brackets

Angle Brackets

Brackets are used in mathematics in a variety of notations, including standard notations for commutators, the floor function, the Lie bracket, equivalence classes, the Iverson bracket, and matrices. Square brackets may also represent intervals; ]0, 5[ for example, is the interval between 0 and 5, not including 0 or 5 (sometimes written (0,5)).

Curly Brackets

Below is an overview of a computer keyboard with the open curly bracket and close curly bracket keys highlighted in blue. How to create an open and close curly bracket. Creating the '{' and '}' symbols on a U.S. keyboard. On English keyboards, the open bracket and close bracket are on the same key as the square bracket keys close to the Enter key.

Double Brackets

Coxeter and Johnson, use square brackets to mark of a symmetry, eg [3,3] is the symmetry of {3,3}, but use double-square brackets to add a secondary extension ie [[3,3]] is the tetrahedral symmetry, along with swapping a figure and its dual.

image: lowes.com
Floor and Ceiling Corners

The ceiling function is usually denoted by ceil(x) or ceiling(x) in non-APL computer languages that have a notation for this function. The J Programming Language, a follow on to APL that is designed to use standard keyboard symbols, uses >. for ceiling and <. for floor.

Lenticular Brackets

The idea of “bracket-like” characters might be more or less be identified with the General Category (gc) property values of Ps (Punctuation, open) and Pe (Punctuation, close). This category contains a few dozens of paired punctuation marks, mostly excluding quotation marks (categories Pi and Pf).

image: charbase.com
Parentheses

Parentheses. You’re probably well versed in how to use those sideways eyebrow thingies, better known as parentheses. First, remember that a pair of them is called “parentheses,” whereas a single one is a “parenthesis.” You may want to review episode 222 in which we compared parentheses to dashes and commas.

Quine Corners and Half Brackets

=== Quine corners and half brackets === The Quine corners ⌜ and ⌝ have at least two uses in mathematical logic: either as quasi-quotation, a generalization of quotation marks, or to denote the Gödel number of the enclosed expression.

Square Brackets

Parentheses and brackets ( ) [ ] Round Brackets Round brackets (also called parentheses, especially in American English) are mainly used to separate off information that isn’t essential to the meaning of the rest of the sentence.