Dec 14, 2025 · Both 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 …

Jul 21, 2020 · Is 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 ...

Sep 5, 2012 · This 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 …

Jun 11, 2025 · 6 "Every metric is continuous" means that a metric d d on a space X X is a continuous function in the topology on the product X × X X × X determined by d d.

Jan 27, 2014 · To 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 …

Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago

Sep 9, 2024 · The Cantor function is a standard example of a function f: [0, 1] → R f: [0, 1] → R that is continuous, has almost everywhere zero derivative, and nonetheless is not constant. More …

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a piecewise continuous

Jul 18, 2015 · Continuous function from $ (0, 1]$ onto $ (0, 1)$? Ask Question Asked 11 years, 2 months ago Modified 10 years, 6 months ago

May 10, 2019 · Of course, the CDF of the always-zero random variable $0$ is the right-continuous unit step function, which differs from the above function only at the point of discontinuity at $x=0$.