Continuous vs Discrete Variables - Mathematics Stack Exchange
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 …
What is a continuous extension? - Mathematics Stack Exchange
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 …
Difference between continuity and uniform continuity
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 …
A short proof that if $f$ is continuous then $f^ {-1}$ 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.
What's the difference between continuous and piecewise continuous ...
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
Understanding Lipschitz Continuity - Mathematics Stack Exchange
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. …
real analysis - Midpoint-convexity and continuity implies convexity ...
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 …
general topology - Continuous selection from an upper hemicontinuity ...
Nov 17, 2024 · Roughly, UHC correspondences admit approximations, i.e. continuous selections of the epsilon-enlargement of the graph, whereas LHC correspondences are better behaved for getting …
Continuous function defined on compact set is uniformly continuous
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
Continuous functions that are not uniformly continuous.
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 …