http://www.bing.com:80/search?q=Continuous+Learning+and+DevelopmentSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Continuous+Learning+and+DevelopmentCopyright © 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 ...Mon, 06 Apr 2026 00:47:00 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 $\mathbb R$.Mon, 06 Apr 2026 11:17:00 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 ...Sun, 05 Apr 2026 17:52:00 GMThttps://math.stackexchange.com/questions/191268/absolutely-continuous-functionsThis might probably be classed as a soft question. But I would be very interested to know the motivation behind the definition of an absolutely continuous function. To state "A real valued function...Fri, 03 Apr 2026 21:01:00 GMThttps://math.stackexchange.com/questions/4847031/prove-or-disprove-that-for-a-continuous-random-variable-cdf-is-continuousWith your definition, it's not true: mixture of, say, normal and discrete variables has range $\mathbb R$, but it's CDF isn't continuous. The standard name for random variables that have PDF is absolutely continuous, but some sources omit "absolute". I don't think the property "range is continuum" (what exactly it means? that is has cardinality continuum, or that it is continuum in topological ...Sun, 05 Apr 2026 02:00:00 GMThttps://math.stackexchange.com/questions/75491/how-does-the-existence-of-a-limit-imply-that-a-function-is-uniformly-continuousThen the theorem that says that any continuous function on a compact set is uniformly continuous can be applied. The arguments above are a workaround this.Sat, 04 Apr 2026 19:34:00 GMThttps://math.stackexchange.com/questions/569928/prove-that-the-function-sqrt-x-is-uniformly-continuous-on-x-in-mathbbr@user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly continuous.Fri, 03 Apr 2026 13:01:00 GMThttps://math.stackexchange.com/questions/3831023/can-a-function-have-partial-derivatives-be-continuous-but-not-be-differentiableBy differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.Wed, 01 Apr 2026 17:50:00 GMT