Hi this is a very short question, I'm afraid this post might get deleted because it's too short. I was wondering if this is true: (in an intro analysis course)
$$\forall x,y\in\mathbb{R},\ \ \sup(f(x)-f(y))\leq |f(x)-f(y)|$$ Is this inequality always true?
If it is could someone show me a proof of this? Thank you!