Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [big-list]

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

1419 questions
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Easy proof of $\mathcal{P}(\mathbb{Q})$ is uncountable [Big list]

I'm looking for a easy proof of uncountability of $\mathcal P(\mathbb Q)$. I'll contribute with this: Let $\mathcal{P}(A)$ denote the power set of $A$, since…
L F
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Is there plane curves with limit number of operations in which is non-constructible and how do we prove it

Is there plane curves with limit number of operations in which is non-constructible and how do we prove it is non-constructible, i call it non-constructible if we have to plot infinity number of point in order to obtain for every part of curve, for…
Victor
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Good book on Lebesgue Theory

I am a graduate student and I need a suggestion for a good book in Lebesgue Measure Theory with good exercises and if its possibly with hints or solutions. Thank you.
spyros
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Uniform convergence in series definitions of functions

Are there examples of well-known functions which are defined as the limit of a sequence of functions (for example, power series definitions) and are not uniformly convergent? Thanks!
velut luna
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Different Types of Waves

I am making a basic 2D rigid body simulator as a hobby. It involves springs. Naturally, I need to render them. Rigid body simulators, such as Algodoo, render them simply like this Another (more common) helical representation And many more... So,…
AvZ
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Different ways to prove convexity of quadratic form associated to rank 1 matrix

Let $v \in \Bbb R^n$, and $f:\Bbb R^n \to \Bbb R^n$ with $f(x)=\langle x,(vv^T)x\rangle$. Show that $f$ is convex. I'm looking for different approaches to solve this (rather simple) problem. Every tools are allowed. This is one solution: The…
Hello
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Why $1$ isn't a prime?

I was wondering the reason behind defining the Prime Numbers in a manner of which $1$ isn't an example. I read in Rotman's A First Course in Abstract Algebra that one reason that $1$ is not called a prime is that many theorems involving primes would…
user170039
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List of functions $\chi_{s,a}(n)$ defined on a Group such that $\chi_{s,a}(n)\in{s,a}$ and depending on the parity

Question Let $(G,\cdot,e)$ be a non-commutative group and $s,a \in G$ .I'm looking for interesting functions $\chi_{s,a}:\Bbb N \rightarrow G$ witht this property $$\chi_{s,a}(n)= \begin{cases} s, & \text{if $n$ is even} \\ a, & \text{if $n$ is…
MphLee
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Crazy Set Theory Analogies

I think the following analogies are too interesting to be ignored: Union = Least Common Multiple If $G_1,...,G_n$ denote a number of sets of points (either linear or in any number of dimensions), the set which contains every point that belongs to…
bolbteppa
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A big list of examples that a power of a prime ideal is not primary in an algebra of finite type over a field

Let $k$ be a field. Let $A$ be an integral domain which is a $k$-algebra of finite type. I would like to know examples that a power of prime ideal of $A$ is not primary. The more example, the better. In other words, I'm asking a big list of such…
Makoto Kato
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What is the best book for the following mentioned courses?Internet resources too please.

1.Motivation:Learning physics and computer science and of course the enchantment of maths itself. 2.Background:A little bit of algebra,Trigonometry utmost basics and basic geometry 3.Why it is interesting and why it should be answered? Honestly it…
Neelesh V
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Best graphing program for Mac or PC?

I just bought the highest end iMac, with a student discount, of course, and was wondering what is the best graphing program out there. A program that can graph any equation that I throw at it AND one where I can manipulate variables such as the…
transcendental
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Applications for the order of an element in a group G

Can someone give me concrete applications for the order of an element in a group G? I found a lot of properties/lemmas of it but no concrete applications.
Ayoub Rossi
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Discrepancies in mathematical definitions.

What are some examples where there is a discrepancy in the mathematical definition of a term? For example : $\bullet$ Isosceles triangle: "exactly two sides are equal" or does it say "minimum two sides are equal"? $\bullet$ Binomial Coefficient: $…
AryanSonwatikar
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What mathematics cannot be reduced to pigeonhole?

Pigeonhole is a fundamental principle without which state of mathematics will be much different. However what examples of good mathematics has not yet been proved and cannot be proved with pigeonhole alone?
Turbo
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