Apr 27, 2018 · I'd like to mention that from a pedagogical standpoint the "analysis" definition of continuity is more useful for teaching analysis students than the "intro to calculus" definition even though they …

Jan 17, 2012 · This should hold for every (positive) epsilon, in particular for positive epsilons close to zero (note that if this holds for a given epsilon, it also holds ipso facto for every larger epsilon).

Jan 16, 2016 · On the other hand, compactness is a generalization, in some sense, of finite sets. i.e., compact sets have many properties plausibles in finite sense.

This question is for me to better understand the beginning of a real analysis course. We are provided with two definitions of supremum as follows: Def 1 : Let $S$ be ...

Apr 27, 2019 · In particular, the strongly monotonically increasing condition, for example, formalizes this idea of "don't look back." This definition enables some useful results we like - for example, this …

Wikipedia provides several different definitions of connectedness that they say are equivalent. For example, it says that a connected set is not the union of disjoint open sets. While this makes se...

Feb 21, 2015 · In other words, your teacher's definition does not say that a sequence is bounded if every bound is positive, but if it has a positive bound. The sequence $ (0,0,\ldots)$ has indeed a positive …

Aug 7, 2017 · But I find it to be confusing, as from the above definition of convergence, $1/n$ turns out to be a Cauchy sequence. But wikipedia seems to be providing a different definition of convergence …

Aug 17, 2020 · I would like to ask probably a small question. I am reading Brown-Churchill complex variable book. There it is defined that contour is a piecewise smooth arc, where smooth arc is a …

Jan 3, 2020 · 2 Because while the definition "differentiable in a neighborhood" is a suitably- equivalent way of saying "analytic" in the context of complex analysis, it is not necessarily the most informative …