Apr 17, 2016 · As I have always understood it (and various online references seem to go with this tradition) is that when one says a function is increasing or strictly increasing, they mean it is doing so …

Let x1> 1 x 1> 1 and let xn+1:= 2 − 1 xn x n + 1:= 2 1 x n for n ∈ N n ∈ N. Show that (xn) (x n) is bounded and monotone. Find the limit. I am confused on how to show that the sequence is …

Dec 16, 2013 · If you want to prove the statement, if a sequence is monotone and bounded then it converges, the logically equivalent contrapositive would be, if a sequence is divergent then either it is …

Let f be a monotone function on the open interval (a,b). Then f is continuous except possibly at a countable number of points in (a,b). Assume f is increasing. Furthermore, assume (a,b) is bou...

Aug 28, 2023 · (Monotone differentiation theorem) Any function F:R → R F: R → R which is monotone (either monotone non-decreasing or monotone non-increasing) is differentiable almost everywhere. …

Dec 13, 2025 · In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was …

Oct 6, 2025 · I am from a non-English speaking country. Should we say monotonous function or monotonic function?

In words, it is a monotone class containing the algebra $\mathcal A$. Since $\mathcal M$ is the smallest monotone class containing $\mathcal A$, it must be contained in any other monotone class …

A function is convex if and only if its gradient is monotone. Ask Question Asked 9 years, 9 months ago Modified 1 year, 7 months ago

4 I am trying to prove this theorem "every sequence has a monotone subsequence" I found this proof Proof: Let us call a positive integer n n a peak of the sequence if m> n xn>xm m> n x n> x m i.e., if …