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20250911170650 Lipschitz Continuous permanent 2025-09-11T21:06:50Z 2025-09-16T16:32:37Z

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.