Intiution Behind Lipschitz continuity

so you know, you defintly have heard about Lipschitz continutiy in fields of deep leanring or contorl systems, at first I didn’t grasp why this have its own name and what is really behind its defention, it was really confusing, so after some look around and see, here is the intiution I grasped:

it is basically saying the derivitaive of function is bounded but it also have some more intution

Sources

• https://math.stackexchange.com/questions/345212/lipschitz-continuity-and-slope
• https://math.stackexchange.com/questions/353276/intuitive-idea-of-the-lipschitz-function
• https://ai.stackexchange.com/questions/30304/what-does-it-mean-having-lipschitz-continuous-derivatives
• https://math.stackexchange.com/questions/755233/how-to-compute-the-lipschitz-constant-for-the-multivariate-function-fx-y-1-xy