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
terminology - Is the term *monotone* used fairly consistently to mean . . . Strictly monotone means that the derivative is either everywhere positive, or everywhere negative Monotone increasing (decreasing) means the derivative is everywhere positive (negative) So monotone increasing (decreasing) means strictly monotone Since I wrote that over a decade ago, I don't recall what my source was for that
functional analysis - Characterization of maximal monotone operators . . . Moreover a monotone operator is said to be maximal in the sense of inclusion of graphs (i e the graph of A has no proper monotone extension) Where can I find a detailed proof of this fact? Thank you in advance, I'm really clueless
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
sequences and series - Monotonically increasing vs Non-decreasing . . . Note that the Monotone Convergence Theorem applies regardless of whether the above interpretations: a non-decreasing (or strictly increasing) sequence converges if it is bounded above, and a non-increasing (or strictly decreasing) sequence converges if it is bounded below
Monotone Function on a interval - Mathematics Stack Exchange 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