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 …

To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") simultaneously …

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 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 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 ...

Jan 12, 2015 · 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 …

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

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. You can likely …

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.

I know that the image of a continuous function is bounded, but I'm having trouble when it comes to prove this for vectorial functions. If somebody could help me with a step-to-step proof, that would be great.