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 …

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...

Jan 11, 2011 · Is there a continuous and monotone function that's nowhere differentiable ?

Jun 2, 2020 · I can understand that if $f$ is monotone, then $g$ is monotone by continuous inverse theorem. But is this really necessary for the inverse function theorem to be used?

Green Line: The monotone class generated by A A, which we call M M, is the smallest monotone class containing A A, meaning no other monotone class containing A A is properly contained inside M M.

May 24, 2020 · I am watching a very nice set of videos on measure theory, which are great. But I am not clear on what the motivation is behind the monotone convergence theorem--meaning why we need …

Jan 26, 2013 · Show that a divergent monotone increasing sequence converges to $+\infty$ in this sense. I am having trouble understanding how to incorporate in my proof the fact that the sequence …

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 …

Dec 15, 2019 · The monotone convergence theorem states for sequences of numbers that a monotonic and bounded sequence converges. Is there an analog for a sequence of uniformly-bounded, …