lbrace
Produces a left curly brace character, essential for set notation and mathematical grouping.
Overview
Serves as a fundamental mathematical delimiter used extensively in set theory, function definitions, and mathematical expressions.
- Essential for defining sets using set-builder notation
- Commonly paired with \rbrace to create matched brace pairs
- Used in programming and computer science notation to denote code blocks or scope
- Appears frequently in probability theory for event spaces and conditional statements
- Particularly useful in cases where automatic sizing of braces is needed for complex expressions
Examples
Set builder notation defining a set of even numbers.
S = \lbrace x \in \mathbb{N} : x \text{ is even} \rbrace
Defining a piecewise function with left brace.
f(x) = \lbrace \begin{array}{ll} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{array}
Defining a sequence using set notation.
\lbrace a_n \rbrace_{n=1}^{\infty} = \lbrace 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots \rbrace