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 …

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 …

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 …

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 …

Feb 12, 2022 · Prove that the modulus of continuity is continuous Ask Question Asked 4 years, 1 month ago Modified 1 year, 11 months ago

These functions aren't even defined, I don't see how they could be continuous. What is true is that the set of eigenvalues is continuous (for the right topology on the power set).

Then the theorem that says that any continuous function on a compact set is uniformly continuous can be applied. The arguments above are a workaround this.

The fact that f is continuous doesn't guarantee that the image of f's inverse is open, much less is even defined. For example, f (x) = 1 is continuous but it's inverse isn't even defined. Maybe the argument …

May 11, 2015 · It can be shown that for any 2 functions f and g, if f is continuous on R and g is a linear function with nonzero slope, f ∘ g is continuous so for any positive real number a, if exp (x) is …

Jan 30, 2024 · Can a discontinuous function have a continuous derivative? Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago