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 …

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 …

Mar 3, 2023 · The Weierstrass theorem suggest that in order for a function f f to have a min and max value, the following must hold: f f must be continous over the domain Domain should be …

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

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 …

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 …

Sep 4, 2018 · The Weierstrass theorem from complex analysis states the following: Suppose fn f n is a sequence of analytic functions converging uniformly on an any compact subset of its …

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 …

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 …

Feb 26, 2012 · The Bolzano-Weierstrass theorem states that each bounded sequence has a convergent subsequence. It follows that an unbounded sequence has at least one diverging …