Jun 11, 2021 · Yes but this explanation just shifts the problem from the perspective of limits points to subsequence that converge to them which is an alternative definition of Bolzano-Weierstrass …

Dec 26, 2022 · I would like to show the Bolzano-Weierstrass in $\mathbb {R}^n$, I have seen this theorem in $\mathbb {R}$ and I know it can be shown by induction, something I will try now.

Jun 10, 2011 · As Jyrki points out in the comments to your question, there is not a unique Weierstrass form of an elliptic curve, but a bit more can be said. Given an elliptic curve E/K with Weierstrass form

Apr 8, 2014 · 9 Consider the Weierstrass function: $$\sum_ {n=0}^ {\infty}a^n\cos {b^n\pi x}$$ It is well-known as an example of a function that is everywhere continuous and nowhere differentiable. When …

Sep 3, 2022 · The earliest known Weierstrass’ text where the $\varepsilon$ - $\delta$ technique is mentioned are differential calculus lecture notes made at a lecture read in the summer term of 1861 …

The Bolzano-Weierstrass theorem says that every bounded sequence in $\\Bbb R^n$ contains a convergent subsequence. The proof in Wikipedia evidently doesn't go through for an infinite …

Jul 19, 2023 · The Stone-Weierstrass theorem says that if you have any family of functions that's a subalgebra, containing $1$, and separates points, you can approximate any continuous function …

Oct 1, 2025 · Game theoretic perspective of Landau kernel proof of Weierstrass approximation theorem? I am trying to understand the relationship between Chebyshev approximation theorem and …

Jan 17, 2022 · There is a famous example of a function that has no derivative: the Weierstrass function: But just by looking at this equation - I can't seem to understand why exactly the Weierstrass Function …

The Weierstrass function mentioned in Jesse Madnick's answer is the standard example, but I think this example is slightly misleading. The fact that it is constantly presented as the standard example may …