A function is convex if and only if its gradient is monotone. Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
logic - Meaning of Monotone in Monotone Disjunction - Mathematics . . . The set of slides you link to speaks of "monotone disjunctions" in a particular AI context, and the terse woirding "no negations" makes sense only in this implicit context It is common in this area to consider disjunctive clauses of the form $$ x \lor y \lor \neg z \lor w \lor \cdots \lor \neg u $$ -- that is, a disjunction of input variables
Monotone convergence theorem for series (basic proof) My question is how to prove monotone convergence theorem for infinite series without more advanced technique like counting measure I see this used a lot But looking through books like Rudin, the theorem for series or elementary proof is not to be found The theorem is:
Strong convexity and strong monotonicity of the sub-differential Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers