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.
1,541 questions
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Are there any other special mathematical definitions like $0! =1$ to ensure consistent and valid results?
In mathematics the $0!=1$ to ensure consistency in formulas.
Are there other examples in mathematics where unusual or seemingly odd definitions or conventions are adopted to maintain valid and ...
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Planar geometry problems solved by thinking out of the plane
What are some examples of a planar geometry problem with an elegant nonplanar solution?
I will post one example as an answer.
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(Hidden) symmetries examples in probability
I am looking for some probability problems in which there is a symmetry that you don't notice in the first place, but by noticing it, you can easily get the answer.
I have two examples in mind, and in ...
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Cool constants from continued fractions with Gauß notation
As some of you may know, a not-often-used but really comfy notation for continued fractions is one made by K. F. Gauß, which is similar to a sum or prod operator. For those who don't know it, it is ...
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Simple rules that generate complexity
I'm planning a low-level classroom presentation on the theme of "simple rules that generate complexity". Any ideas?
The one I already have is Pascal's triangle mod 2 (i.e., with entries in $\...
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Constructions of regular languages
Fix a finite alphabet $A$. The set of regular languages is the smallest set of languages on $A$ (i.e. subsets $L$ of the free monoid $A^*$) containing $\varnothing$ and the singletons $a$ for $a\in A$ ...
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Concrete applications of localization at primes to motivate deeper abstract study of localization?
There are already lots of posts on this site about motivating localization:
Motivation of Localization "Let's start with the idea of "just looking at functions in small neighborhoods of a ...
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What 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 $...
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List of Results Provable in Absolute/Neutral Geometry?
I'm looking for a list of results that can be proven using the axioms of Euclid's Elements, but without using the parallel postulate, either explicitly or implicitly. From my search so far, I've ...
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Unique tetrahedral representations $n = \frac{a(a+1)(a+2) + b(b+1)(b+2) + c(c+1)(c+2)}{6}$
Consider strict positive integers $n$
Some of those have a unique representation as a sum of $3$ positive tetrahedral numbers :
$$n = \frac{a(a+1)(a+2) + b(b+1)(b+2) + c(c+1)(c+2)}{6}.$$
Lets assume ...
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What are some unsolved problems in group theory which can be explained to a beginner?
I'm interested in unsolved problems in group theory, which are easy enough to state to a beginner. This question is very much in the same spirit as this similar question about calculus.
A problem ...
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A list of famous linear operators? [closed]
I'm interested in a vast list of linear operators defined on functional spaces. I know some of the classical ones. For instance:
$$ \textbf{Bernstein operators.} \qquad B_n (f,x)= \sum_{k=0}^n f\left( ...
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Interesting Hilbert Spaces
I am looking for interesting Hilbert spaces / Hilbert spaces that are important for certain applications (e.g., partial differential equations). I am aware of the following Hilbert spaces:
The ...
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Soft question - Uncommon examples of linear operators [closed]
Common examples of linear operators are
Matrices in finite dimensional spaces.
Differentiation and definite and indefinite integration in appropriately regular functional spaces.
I remember that the ...
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Inclusions $\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$ as "saving-time constructions"
When a teacher wants to justify the construction of an extension of numbers $E \subset E'$, he usually states a problem in $E$, that is not solvable in $E$ and that therefore requires the construction ...
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