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 …
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
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 …
Absolutely continuous function on R - Mathematics Stack Exchange
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...
Must probability density be continuous? - Mathematics Stack Exchange
May 26, 2012 · From other materials that I've read, the probability density of a continuous random variable must itself be continuous. Is this correct? If it is, I don't understand why that would be so, …
real analysis - Prove that every convex function is 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 …
calculus - Are all continuous one one functions differentiable ...
Apr 14, 2015 · Which is continuous and one-to-one on $\mathbb R$, but is not differentiable at $0$. This is of course just one example, but in general, any time you "stick" two functions together at a point …
Is there any intuition for continuous embeddings?
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 …
Continuous Poisson Distribution - Mathematics Stack Exchange
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 …