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 …

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 …

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.

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).

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 …

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 …

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 …

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 …

Jul 27, 2024 · In fact, it turns out that every continuous function from a path connected space to $\mathbb R$ is a quotient map Note that the closed map lemma cannot be generalised, for example …

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 …