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

Nov 9, 2024 · I learned a theorem that if $f$ is continuous and bijective then $f^ {-1}$ is continuous. I went online to search for a proof and saw a really long proof in this link.

Dec 20, 2015 · What is the definition of absolute continuity in whole $\\mathbb{R}$. I know the definition on an interval $[a, b]$. I have a trouble with understanding the definition of absolute continuity in who...

Nov 21, 2016 · Matrices with continuous indices Ask Question Asked 9 years, 2 months ago Modified 9 years, 2 months ago

Dec 26, 2025 · Let (X, n) (X, n) be normed space and B B a basis (by basis I mean a set of vector such that every vector in X can be expressed in an essentially unique way as a finite linear combination of …

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 $d$.

Mar 10, 2021 · The apostrophes around "continuous product" indicate OP is using that terminology in a looser sense to convey the idea of multiplying over a "continuous family" of factors, much like …