How pathological can a computable real function be?
Call a function $f:\Bbb{R} \to \Bbb{R}$computable if there is an algorithm that can calculate $f$ in any desired precision. Formally, this means that there exists a Turing machine that, given an input...
View Article"Are there any simple groups that appear as zeros of the zeta function?" by...
I would like to understand the "upsetting"-to-mathematicians nature of this question Freyd poses to demonstrate that "any language sufficiently rich that to be defined necessarily allows you to...
View ArticleIs the norm of first or second level of of signature a convex function?
This question is related to the signatures that arises in rough path theory. https://en.wikipedia.org/wiki/Rough_pathIs there any reference to understand if the norms of the different levels of...
View ArticleI'm turning 18 soon, and I don't know how to do anything regarding college...
I'm sorry for how long, whiny, and pointless this will feel. I have not been able to find anyone aside from therapists to discuss any of this with, and I need advice from people who actually know what...
View ArticleTranspose method for finding a basis for the row space
My linear algebra textbook outlines a method of finding a basis for the row space of a matrix by finding a basis for the column space of its transpose. Is there any point of using this method? It seems...
View Article"So That" vs. "Such That"
In definitions and exercises, I notice that "so that" and "such that" are seemingly used interchangeably. Are they in fact interchangeable, or is one more appropriate for a specific context?Note:...
View Article(Im)possibility of closed-form expression of Clausen functions
When I started learning Riemann zeta function, I was fascinated that $\zeta(2n)$ can be expressed with finite integers and $\pi$ while $\pi$ has no obvious relation with the sum-$\zeta(2n)$ but no...
View ArticleAre there terminologies for "one-to-one" but not "onto" functions, and "onto"...
One-to-one (injective) functions are not necessarily not onto (not surjective).Similarly, onto functions are not necessarily not one-to-one.So, a function can be one-to-one and onto...
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Search for more theorems like Orthocentric System
Earlier, I was very impressed with the idea of ​​The Orthocentric System. With regard to four points in the plane, if one of these points is the point of intersection of the heights in the triangle...
View ArticleWhat makes a mathematical theorem research paper worthy? Is it purely...
There are infinitely many theorems of mathematics, but only a tiny portion of them are interesting enough to be publishable in a research journal. Is the criterion for which theorems are interesting...
View ArticleIntuition for idempotents, orthogonal idempotents?
Given a ring $A$, an element $e \in A$ is called an idempotent if one has $e^2 = e$. If $e$ is an idempotent, then so is $1 - e$, since$$(1 - e)^2 = 1 - 2e + e^2 = 1 - 2e + e = 1 - e.$$Also, we have...
View ArticleHow hard is this book: Mathematical Puzzles [closed]
I am a beginner in puzzle solving and competition mathematics and I came across this book called mathematical puzzles by peter winkler. I find the reasoning in the book quite challenging and thus...
View ArticleA reference on Total Variation and its applications in Image Processing
The title is almost self-explanatory; I need a beginners' readable reference (book or article) on total variation and its applications in image processing, know any?Thanks bunches.
View ArticleImpact of homotopical algebra on homological agebra
I was recently reading through Dwyer and Spalinski's notes introducing model categories. In it is shown a different way to describe $Ext(A,B)$ in homotopical terms (see proposition 7.3, I am not...
View ArticleAre there interesting rings without unity?
There are several introductory textbooks which define a ring without any reference to a unity. However, nearly all of the rings one encounters in various branches of mathematics are endowed with a...
View ArticleReverse question of superposition of waves
This is a soft question.Consider two Gaussian like pulse waves with different heights, means and variances, and there is an overlap between them. By the principle of superposition, they form a new...
View ArticleDegree with which a polynomial changes with some small change
Soft question: I was curious as to how one could measure the degree with which a polynomial is perturbed. More formally, let $P(x) \in \mathbb{C}$ be a polynomial and $\epsilon$ be a very small number,...
View Article"Predicate" vs. "Relation"
What's the difference between a predicate and a relation? I read the definition that an $n$-ary predicate on a set $X$ is a function $X^n\to \{\text{true}, \text{false}\}$ where $\{\text{true},...
View ArticleAre there graphs with multiple edge sets?
I've tried looking this up here and on google, but I think I may not be using the right words. I'm not talking about a mutligraph (multiple edges between the same nodes) or a hypergraph (multiple nodes...
View ArticleWhy rationalize the denominator?
In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$. An answer on this site says that "there is...
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