Is there such a new notion of weakly sequentially continuous in the literature?
Let $G:X \rightarrow Y$ be a continuously differentiable nonlinear operator, with $X$ and $Y$ being real Hilbert spaces. I want to know what is the weakest hypothesis necessary to guarantee that, for...
View ArticleWhat are the arguments of the mathematicians who objected against the...
Q:What are the arguments of the mathematicians who objected against the ontological argument/proof Gödel offered?$$\begin{array}{rl} \text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall...
View ArticleGood books about random walks on groups.
I am about to start writing an undergraduate essay that will be split into two parts - the first part being an introduction to random walks and the second part being about random walks on finite...
View ArticleWhy is the Monster group called that?
This is a bit of a soft question, but why is the Monster group called that? Does it have any connection with monster models in model theory? I would be interested to learn who came up with that...
View ArticleThe sum of multiple irrational numbers can be rational, even when they're not...
From my observation, a sum of a series of irrational numbers can be rational, even when none of them "cancels out" the irrational part of another. Consider the following sum:$$\sum_{n=1}^9...
View ArticleMathematical induction, is it really a proof of truth?
This soft question is, I think, borderline mathematical philosophy.One of my former professors used to say that induction does not prove that a statement is true, but it merely eliminates the...
View ArticleA New Idea: Representing $x/0$ On The Number Line [closed]
Before you downvote, it is my humble request: "please read this thoroughly once."I have a got a new idea to represent $\frac{x}{0}$ on the number line. First, take a look at this new number line given...
View ArticleGeometrical Mathematics Book Recommendation
I'm currently working on a project which requires us to take complex 3D shapes (models of tools) in a STEP file format, which is built from mathematical geometric objects, to represent a shape, and...
View ArticleWhat is the website that returns expression and approximation when we enter a...
I remember a website where I entered like 0.2954 and it returned"It's maybe $sin(0.3)$ ad $\varepsilon=0.001$any help ?
View ArticleBooks to help me research on number theory. [closed]
I am confused and I lack knowledge to decide which book is suitable for me for understanding number theory more.
View ArticleNull law and Nullary intersection
I have been thinking of a problem that I could not get the most satisfying answer yet.The problem I have been thinking of:We know that the Null law says:$$A\cap \varnothing = \varnothing$$but...
View ArticleIndefinite double integral
In calculus we've been introduced first with indefinite integral, then with the definite one. Then we've been introduced with the concept of double (definite) integral and multiple (definite) integral....
View ArticleMathematical research outside academia
My goal up through grad school had been to spend my life doing academic, research mathematics. I got screwed by my advisor and department, though, so that hasn't worked out. I would nevertheless still...
View ArticleTrying to understand spectral geometry
Currently I'm studying Riemannian Geometry, in particular I started to learn something about spectral geometry like the famous results of Lichnerowicz and Obata about the first eigenvalues of a closed...
View ArticleIs Gamma function just an analytical continuation of factorial or is there more?
Factorials are the number of arrangements of things. Is there a similar interpretation for the Gamma function or is it just an extension of factorials? Does $\left(\frac{1}{2}\right)!$ mean anything??...
View ArticleWhat is the use of scheme theory?
I should preface this by saying that my background in Algebraic Geometry is (more or less) the content of Vakil's notes up through Chapter 4 (i.e. through the definition of a scheme and several...
View ArticleHow to propose a conjecture
What are the basic things (about when and how) to be kept in mind while proposing a conjecture in Mathematics. Should it accompany solid efforts at proof. When should any one think of proposing a...
View ArticleHow to submit a conjecture for review?
I was recently attempting to solve one of the more known, already proved, problems in mathematics when I stumbled across an observation I thought might be worth digging into further. Unfortunately I...
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 ArticleSearching a Proof for Lusternik-Schinerlmann theorem on geodetics [closed]
Currently I'm studying Riemannian Geometry and I found the following statement by Lusternik and Schnirelmann:"Every riemannian metric on the 2-sphere admits at least $3$ geodesics"I found this theorem...
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