Totally balanced hypergraphs on $n$ vertices
Let $H=(V,E)$ be an hypergraph, where $V$ is the vertices set and $E$ is the hyperedge set. A special cycle of $H$ is a sequence$(v_1, e_1, v_2, e_2, \ldots, v_{k}, e_{k})$,with $k \geq 3$, where $v_i...
View ArticleNewbie seeking structured path to learn Mathematical Logic and Programming —...
I'm a complete beginner who's deeply interested in mathematical logic and programming, especially the kind that helps build logical systems or understand computation at a fundamental level.My goal is...
View ArticleWhat are other surprising results about Dickman's function?
Dickman's function $\rho(x)$ can be defined to be the unique continuous solution of the delay differential equation$$ x\rho'(x)+\rho(x-1)=0\hspace{.7cm} \forall\ x>1$$with the initial condition...
View ArticleHow should I resume studying mathematics after rushing through foundational...
I'm a self-learner who has been studying mathematics independently for a few years. I enjoy math, but I've recently hit a roadblock, and I'm not sure how to move forward. More than a year has passed...
View ArticleGödel's ontological proof and "modal collapses"
Recent findings on Gödel's ontological argument allowed to ultimately establish a couple of things:Gödel's original axiomata are inconsistentScott's variation instead is consistentScott's axioms imply...
View ArticleAre all equations mathematical? [closed]
I was initially thinking of asking this question on the Philosophy stack exchange, but in the end I decided this one would be better. My question is, are all equations mathematical in nature? I don't...
View ArticleDoes the epsilon-delta definition of limits truly capture our intuitive...
I've been delving into the concept of limits and the Epsilon-Delta definition. The most basic definition, as I understand it, states that for every real number $\epsilon \gt 0$, there exists a real...
View ArticleObjective metric to describe skill vs luck in games
There are many games that even though they include some random component (for example dice rolls or dealing of cards) they are skill games. In other words, there is definite skill in how one can play...
View ArticleBicycle tracks and Doyle's 'The Adventure of the Priory School'—really...
Lots of internet sources claim that—in Doyle's Sherlock Holmes story 'The Adventure of the Priory School'—Holmes' reasoning is flawed when it comes to him and Watson discovering some bicycle tracks. To...
View ArticleSuggested books that have an extensive treatment on Summation Notation
at the moment I'm looking for a book that has the following properties:Is accessible to math undergraduates, preferably not much higher than first or second year undergraduates.Treats summation...
View ArticleIs there any English version of Récoltes et Semailles?
I felt like my question isn't appropriate for MO, so I thought maybe I should post it here. I want to read Alexander Grothendieck's "Récoltes et Semailles", but I don't know any French. I can easily...
View ArticleOrder of adjectival properties
In mathematics, how should the adjectives in front of a noun be ordered? Are there conventions? I can think of a few practices:Use stronger adjectives or more specialised properties first, and more...
View ArticleWhy are $n$ zeroes appended at the end of a number when it is multiplied by...
Let us take a simple example where $n=1$. When a single digit number, say $a$ is multiplied by $10^1$, the answer comes out to be "$a0$". If a number is $a_1a_2a_3\dots a_k$, then multiplication with...
View ArticlePhysical or geometric meaning of the trace of a matrix
The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too.Is there any...
View ArticleHow should I approach the exercises in "Theory of Numbers by Niven,...
I’m currently self-studying number theory using An Introduction to the Theory of Numbers by Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery. The book includes a large number of exercises,...
View ArticleReal empirical complexity involved in everyday mathematical formulae? [closed]
I'm not too sure whether this is the right place to ask, but I was wondering if anyone knew of any study on (or had any personal guesses as to) the complexity involved in actual mathematical formulae...
View ArticleIs there a conventional order for writing the commutative parts of an...
This stemmed from an office discussion. Often, when writing expressions, it feels like there is a most natural option between different ways of writing the commutative parts of an expression; for...
View ArticleWhat does "generally" ("in general") mean in mathematics?
Idiomatically, the word "generally" (and the phrase "in general") is obviously commonly used as a synonym for "usually".However, when writing mathematics, I've always used "generally" (for example,...
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A Collection of Bogus Proofs
Hello M.S.E. people,This question is just for fun, don't take it seriously :). We have all encountered Bogus Proofs, which seem logical and reasonable, but they prove some claims which are completely...
View ArticleFunctional analysis on manifolds
The basic object of functional analysis is the topological vector space, so vector spaces with some topology, we can add additional structure by introducing metrics etc, but the underlying object is a...
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