http://www.bing.com:80/search?q=Continuous+Color+WaveSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Continuous+Color+WaveCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/5114829/continuous-vs-discrete-variablesBoth discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. 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.Sat, 28 Mar 2026 22:48:00 GMThttps://math.stackexchange.com/questions/1182795/what-is-the-intuition-for-semi-continuous-functionsA function is continuous if the preimage of every open set is an open set. (This is the definition in topology and is the "right" definition in some sense.) The definitions you cite of semicontinuities claim that the preimages of certain open sets are open, but does not say so about all open sets. Note that $\ { \ {f \in \mathbb {R} \mid f > \alpha\} \mid \alpha \in \mathbb {R} \} \cup ...Tue, 31 Mar 2026 00:54:00 GMThttps://math.stackexchange.com/questions/294683/showing-that-arctan-is-continuousAs such, $\arctan$ is continuous. If you define $\arctan$ by integrals or power series the result is immediate (the first by the Lipshitz continuity of the indefinite integral and the second from the uniform convergence of power series in compact sets)Fri, 03 Apr 2026 02:10:00 GMThttps://math.stackexchange.com/questions/3764351/is-derivative-always-continuousIs the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines to points on a ...Tue, 31 Mar 2026 17:22:00 GMThttps://math.stackexchange.com/questions/7923/are-continuous-functions-always-differentiableAn interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an exercise) in Kechris' Classical Descriptive Set Theory or Royden's Real Analysis.Fri, 03 Apr 2026 12:47:00 GMThttps://math.stackexchange.com/questions/653100/difference-between-continuity-and-uniform-continuityTo understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on $\mathbb R$ but not uniformly continuous on $\mathbb R$.Tue, 31 Mar 2026 18:05:00 GMThttps://math.stackexchange.com/questions/323610/the-definition-of-continuous-function-in-topology22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like that?I mean what kind of property we want to preserve through continuous function?Fri, 03 Apr 2026 09:05:00 GMThttps://math.stackexchange.com/questions/3846641/continuous-functions-that-are-not-uniformly-continuousThe proof of the statement relies on showing that continuous functions defined in an interval are uniformly continuous. As i finished doing that part, I started wondering: what are all the continuous functions that are not uniformly continuous.Wed, 01 Apr 2026 22:07:00 GMThttps://math.stackexchange.com/questions/236907/closure-of-continuous-image-of-closureClosure of continuous image of closure Ask Question Asked 13 years, 4 months ago Modified 13 years, 4 months agoThu, 02 Apr 2026 20:12:00 GMThttps://math.stackexchange.com/questions/258511/prove-that-every-convex-function-is-continuousThe 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. You can likely see the relevant proof using Amazon's or Google Book's look inside feature.Thu, 02 Apr 2026 17:13:00 GMT