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 …

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 …

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 …

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 …

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 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 …

Definition of continuous map Ask Question Asked 12 years, 10 months ago Modified 1 year, 7 months ago

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 …

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 …

Dec 1, 2020 · I have a discussion with a co-worker, he insists on trying to get the mode of a dataset with continuous data, with numbers that go from 0 to 3000. I say that the results are irrelevant because …