There are other ways a function can be a continuous extension, but probably the most basic way (and likely about the only way you'll see in elementary calculus) is that you have a function …

Oct 15, 2016 · A piecewise continuous function doesn't have to be continuous at finitely many points in a finite interval, so long as you can split the function into subintervals such that each …

Jan 27, 2014 · I understand the geometric differences between continuity and uniform continuity, but I don't quite see how the differences between those two are apparent from their definitions. …

$\begingroup$ @user135626: What I wrote is correct. You are misreading it. I'm not saying the derivative is zero, I'm saying that if the derivative exists, the numerator of the difference …

Oct 22, 2017 · Continuous Models : Probabilistic models with continuous sample spaces differ from their discrete counterparts in that the probabilities of the single-element events may not …

Oct 8, 2021 · The regularity of Brownian paths is expressed quite precisely by it being $\alpha$-Holder continuous for all $\alpha< \frac 12$ but not $\alpha$-Holder continuous for $\alpha …

Added @Dimitris's answer prompted me to mention, beyond the fact that the implication on normed spaces indeed is an equivalence, that it's the converse which holds in the wider …

May 14, 2018 · C1 continuous parametric continuity ensured, notice that the magnitude of the vectors are equal Note: I'm using 'Bezier' curves, so tangents will not overlap (2nd tangent is …

Jul 28, 2017 · So as long as K is 0.252 or bigger then this function is Lipschitz Continuous? What if I pick K to be 0.0001 is the function no longer Lipschitz Continuous? To me this is hard to …

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