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 …
real analysis - Are Continuous Functions Always Differentiable ...
Oct 26, 2010 · An interesting fact is that most (i.e. a co-meager set of) continuous functions are nowhere differentiable. The proof is a consequence of the Baire Category theorem and can be found (as an …
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 …
Prove that the function $\sqrt x$ is uniformly continuous on $\ {x\in ...
Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly …
Is the set of non-differentiable points for a singular continuous ...
In view of the correspondence of nondecreasing functions with positive measures, singular continuous functions correspond to singular continuous measures, i.e. an atomless positive Borel measures …
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 …
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 …
The graph of a continuous function is a topological manifold
Sep 18, 2024 · The graph of a continuous function is a topological manifold Ask Question Asked 1 year, 6 months ago Modified 1 year, 6 months ago
Why not include as a requirement that all functions must be …
Jun 20, 2018 · We know that differentiable functions must be continuous, so we define the derivative to only be in terms of continuous functions. But then, the fact that differentiable functions are …
Integral of non-continuous function - Mathematics Stack Exchange
Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 4 months ago Modified 1 year, 4 months ago