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 …

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 …

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...

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 …

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.

Apr 1, 2025 · It's more correct to say that he proved Jensen's Inequality (with arbitrary real weights) for functions which are midpoint convex and continuous. Of course, Jensen's Inequality with two …

Sep 30, 2020 · The proof of the statement relies on showing that continuous functions defined in an interval are uniformly continuous. As i finished doing that part, I started wondering: what are all the …

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 …

Jul 28, 2017 · I have heard of functions being Lipschitz Continuous several times in my classes yet I have never really seemed to understand exactly what this concept really is. Here is the definition. …

Dec 6, 2020 · Continuous function defined on compact set is uniformly continuous Ask Question Asked 5 years, 2 months ago Modified 2 years, 5 months ago