---
id: 20250911170650
title: Lipschitz Continuous
type: permanent
created: 2025-09-11T21:06:50Z
modified: 2025-09-16T16:32:37Z
tags: []
---

# Lipschitz Continuous

Lipschitz continuous functions are a special case of
continuous functions. Lipschitz continuity means that a cone
can be created with slope less than some real number
$K$. 

Fora a real valued function in one dimension, Lipschitz
continuity is defined as:

$$| f(x_1) - f(x_2)| \leq K|x_1 - x_2|$$

Lipschitz continuity can be expanded to vector fields. From
here, we can say that ODE trajectories do NOT intersect, and
that every trajectory is unique. 
