TeXipedia

max

Represents the maximum value in a set or function, displaying it in upright mathematical text style.

Overview

Essential in optimization problems, mathematical analysis, and statistics for finding the highest value among a collection of numbers or expressions.

  • Commonly used in linear programming and constraint optimization.
  • Appears frequently in algorithm complexity analysis (Big O notation).
  • Distinguished from regular text 'max' by proper mathematical spacing and formatting.
  • Often paired with subscripts to specify the domain or constraints of maximization.

Examples

Finding the maximum value in a set of numbers.

max⁡{3,7,2,5,1}=7\max\{3, 7, 2, 5, 1\} = 7 
\max\{3, 7, 2, 5, 1\} = 7

Maximum function with subscript indicating the domain.

max⁡x∈R(x2−4x+3)\max_{x \in \mathbb{R}} (x^2 - 4x + 3) 
\max_{x \in \mathbb{R}} (x^2 - 4x + 3)

Maximum likelihood estimation in statistics.

L(θ)=max⁡θ∈Θ∏i=1nf(xi∣θ)L(\theta) = \max_{\theta \in \Theta} \prod_{i=1}^n f(x_i|\theta) 
L(\theta) = \max_{\theta \in \Theta} \prod_{i=1}^n f(x_i|\theta)