http://www.bing.com:80/search?q=Continuous+Variable+MathSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Continuous+Variable+MathCopyright © 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/4515004/what-is-the-formal-definition-of-a-continuous-functionThe MIT supplementary course notes you linked to give — and use — the following (non-standard) definition: We say a function is continuous if its domain is an interval, and it is continuous at every point of that interval. (Continuity of a function at a point and on an interval have been defined previously in the notes.) This is actually a useful and intuitive concept, but unfortunately it ...Mon, 06 Apr 2026 05:19:00 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.Sun, 12 Apr 2026 14:02:00 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...Thu, 09 Apr 2026 21:51:00 GMThttps://math.stackexchange.com/questions/339289/continuous-function-proof-by-definitionMore frustratingly, the people giving the answers make bigger mistakes or have bigger confusions about continuity than the person asking for continuity: for a detailed explanation on how to show that the square root function is continuous, here is a Pdf file that gives a detailed example.Fri, 10 Apr 2026 10:08:00 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, 11 Apr 2026 22:03:00 GMThttps://math.stackexchange.com/questions/658450/what-is-the-difference-between-discrete-and-continuous-mathematicsSome people like discrete mathematics more than continuous mathematics, and others have a mindset suited more towards continuous mathematics - people just have different taste and interests. On the other hand, the different areas of mathematics are intimately related to each other, and the boundaries between disciplines are created artificially.Sun, 12 Apr 2026 18:20:00 GMThttps://math.stackexchange.com/questions/477/cardinality-of-set-of-real-continuous-functionsThe cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its values on all the rational points. Since the rational points are dense, this determines the function.Mon, 13 Apr 2026 14:29:00 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, 10 Apr 2026 14:33:00 GMThttps://math.stackexchange.com/questions/930780/is-a-differentiable-function-always-continuous9 Continuous Functions are not Always Differentiable. But can we safely say that if a function f (x) is differentiable within range $ (a,b)$ then it is continuous in the interval $ [a,b]$ . If so , what is the logic behind it ?Sun, 12 Apr 2026 04:51:00 GMT