Mathematical Operations:
- Brackets indicate the order of operations. For example, `(3 + 4) - 5` calculates`(3 + 4) = 7` first, then multiplies by 5.
Grouping:
- Brackets group expressions together, allowing for calculations to be performed on the group as a whole. For example, `(x + y) - (a + b)` calculates `x - a + x - b + y - a + y - b`.
Subscripts and Superscripts:
- Brackets are used to indicate subscripts and superscripts. For example, `x_i` represents the ith element of x, and `x^2` represents x squared.
Set Notation:
- Curly braces are used to enclose elements of a set. For example, `{1, 2, 3}` represents the set containing 1, 2, and 3.
Function Notation:
- Brackets are used to enclose the argument of a function. For example, `f(x)` represents the value of the function f at x.
Interval Notation:
- Brackets are used to define intervals. For example, `[a, b]` represents the interval from a to b, and `(a, b)` represents the interval from a to b (excluding a and b).
Programming Languages:
- Brackets are used in many programming languages for various purposes, such as:
- Parentheses: Enclose method calls, function arguments, and expressions.
- Square brackets: Access array elements, represent arrays or lists.
- Curly braces: Define code blocks, objects, and dictionaries.
Text Formatting:
- Brackets are used in some text formatting conventions:
- Angular brackets: `<` and `>` enclose HTML tags.
- Square brackets: `[` and `]` enclose Markdown links.
- Curly braces: `{ }` enclose placeholder text in templates.
Other Uses:
- In linguistic notation, brackets enclose phonetic transcriptions.
- In music notation, brackets indicate chords or overlapping notes.
- In design and engineering, brackets are used to indicate structural elements.