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 4, 2026 · I was trying to formalize some things about string motion in physics so I could answer more general questions about it and then I got to a point as to see the limit written below. I then …

Jul 22, 2010 · The cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its …

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 …

Apr 13, 2014 · Continuous and Differentiable on the closed interval. This is strictly weaker than the original theorem, and therefore is of course true. But since the theorem also holds if we require …

The space of bounded continuous functions is not separable Ask Question Asked 13 years, 4 months ago Modified 3 months ago

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

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 …

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.

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 …