TeXipedia

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={x∈N:x is even}S = \lbrace x \in \mathbb{N} : x \text{ is even} \rbrace 
S = \lbrace x \in \mathbb{N} : x \text{ is even} \rbrace

Defining a piecewise function with left brace.

f(x)={x2if x≥0−x2if x<0f(x) = \lbrace \begin{array}{ll} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{array} 
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.

{an}n=1∞={1,12,14,18,…}\lbrace a_n \rbrace_{n=1}^{\infty} = \lbrace 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots \rbrace 
\lbrace a_n \rbrace_{n=1}^{\infty} = \lbrace 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \ldots \rbrace