TeXipedia

le

Represents less than or equal to in mathematical expressions and logical comparisons.

Overview

Essential for expressing mathematical inequalities and constraints across numerous fields including mathematics, computer science, and engineering.

  • Commonly used in optimization problems and mathematical proofs
  • Appears frequently in set theory to define ranges and bounds
  • Critical in expressing mathematical constraints and conditions
  • Often paired with other comparison operators in systems of inequalities

Examples

Expressing a less than or equal to relationship between variables.

x≤yx \le y 
x \le y

Defining the domain of a function with a maximum bound.

f(x)=2x+1,x≤5f(x) = 2x + 1, \quad x \le 5 
f(x) = 2x + 1, \quad x \le 5

Specifying inequality constraints in an optimization problem.

minimize z=x+y subject to x+2y≤10\text{minimize } z = x + y \text{ subject to } x + 2y \le 10 
\text{minimize } z = x + y \text{ subject to } x + 2y \le 10