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 …

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

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 …

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

Aug 25, 2021 · There are different types of continuous extensions of Poisson distribution. I favor the one presented in this paper: "Continuous counterparts of Poisson and binomial distributions and their …

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.

Showing that a function is not continuous Ask Question Asked 8 years, 11 months ago Modified 7 years, 4 months ago

Jan 1, 2026 · Let X, Y X, Y be topological spaces and X ⊂ Y X ⊂ Y. X X is said to be continuously embedded in Y Y if the inclusion map i: X → Y i: X → Y, x ↦ x x ↦ x, is continuous. The definition …

On the smaller closed interval the derivative is bounded; on the entire open interval the function does have vertical asymptotes and cannot be uniformly continuous. Re Dan Fisher's example of $\sqrt x …