Continuous run unloader valve. sufficient condition) the function is differentiable at that point. I am quite aware that discrete variables are those values that you can count while continuous variables are those that you can measure such as weight or height. Mar 6, 2021 · If it's continuously differentiable then it's continuous. Jan 30, 2024 · Can a discontinuous function have a continuous derivative? Ask Question Asked 2 years, 1 month ago Modified 2 years, 1 month ago Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. This is of course just one example, but in general, any time you "stick" two functions together at a point where their derivatives are not equal, like in my example, you can cause the resulting function to have a point at which it is not differentiable. Jan 8, 2017 · The reason one refers to this as "continuous spectrum" Historically had nothing to do with continuity; such spectrum was found to fill a continuum, rather than being discrete. Dec 18, 2025 · I was recently going through General Topology by N. You can likely see the relevant proof using Amazon's or Google Book's look inside feature. Jan 30, 2024 · Can a discontinuous function have a continuous derivative? Ask Question Asked 2 years, 1 month ago Modified 2 years, 1 month ago. e. Bourbaki, and found the following definition of topological groups acting continuously on topological spaces (slightly rephrased) : A topological Apr 14, 2015 · Which is continuous and one-to-one on $\mathbb R$, but is not differentiable at $0$. All continuous functions are absolutely continuous on a compact set. At risk of contradicting this assessment, not all subsets of the real line are intervals, and there are important examples and non Sep 9, 2024 · The post Is the set of non-differentiable points for a singular continuous function nowhere dense? also seems highly relevant, but I can't parse the answer enough to figure out whether it addresses my particular point. Sep 18, 2020 · By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i. Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective domain. However, that comment cites a link that seems to be broken, and I haven't found this statement mentioned in other places. Jun 24, 2016 · So one may note that the only functions whose uniform continuity is really interesting to investigate, are the ones defined on an unbounded interval, being globally continuous, non-periodic and non-differentiable on an unbounded subinterval of their domain. tmbgmx szreg cznw vgwazhha lrcnu hduty nmqt oezoyhao lhnkh ikue