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 …
What is a continuous stochastic process? - Mathematics Stack Exchange
Aug 4, 2022 · Isn't this violating the definition of continuous stochastic process or is it that I have to keep $\omega$ constant throught out the process ? Also, is $\omega$ in the definition of continuous …
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 …
Can a function have partial derivatives, be continuous but not be ...
Sep 18, 2020 · By differentiability theorem if partial derivatives exist and are continuous in a neighborhood of the point then (i.e. sufficient condition) the function is differentiable at that point.
If function is differentiable at a point, is it continuous in a ...
Jul 11, 2020 · The use of the theorem requires that a function is continuous between two points. Hence the motivation for the question, if a function is differentiable at a point, is it continuous in some …
real analysis - How do I show that all continuous periodic functions ...
Apr 30, 2014 · Show that every continuous periodic function is bounded and uniformly continuous. For boundedness, I first tried to show that since the a periodic function is continuous, it is continuous for …
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 …