Proof of Bolzano Weierstrass Theorem in $\mathbb {R}^n$
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.
calculus - Original source of "precise" ε-δ (epsilon-delta) formal ...
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 …
calculus - Why isn't the Weierstrass function $\sum_ {n=0}^\infty a^n ...
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 …
Relationship between the Weierstrass function and other fractals
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 …
In what spaces does the Bolzano-Weierstrass theorem hold?
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 …
real analysis - Generalisation of Stone-Weierstrass Theorem / Fourier ...
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 …
Weierstrass theorem on determining if function have min and max
Mar 3, 2023 · Weierstrass theorem on determining if function have min and max Ask Question Asked 2 years, 9 months ago Modified 2 years, 9 months ago
Intuition for Bolzano-Weierstrass Theorem - Mathematics Stack Exchange
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 …
analytic functions - The Weierstrass theorem from complex analysis ...
Sep 4, 2018 · The Weierstrass theorem from complex analysis states the following: Suppose $f_n$ is a sequence of analytic functions converging uniformly on an any compact subset of its domain to $f$.
Fourier Transform of the Weierstrass Function
Dec 1, 2020 · Fourier Transform of the Weierstrass Function Ask Question Asked 5 years ago Modified 4 months ago