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 …

Sep 2, 2024 · Prove $\ln (x)$ is continuous using $\epsilon-\delta$ Ask Question Asked 13 years ago Modified 1 year, 6 months ago

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 …

Sep 18, 2024 · The graph of a continuous function is a topological manifold Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago

Jan 5, 2016 · As such, $\arctan$ is continuous. If you define $\arctan$ by integrals or power series the result is immediate (the first by the Lipshitz continuity of the indefinite integral and the second from …

Mar 7, 2013 · 22 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it like …

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 …

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 …

Apr 3, 2022 · So you can have continuous functions defined over rationals; but the rationals are not a continuum. Why not? The notion of a continuum has its roots in geometry, and -- in the barest …

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 …