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Burnside lemma and Pólya enumeration theorem examples
Observe that the convention at the OEIS is that the term necklace
refers to the slots being arranged around a circle with rotational
symmetry acting on them. Similarly the term bracelet indicates
reflections acting on the slots in addition to rotations. This is the
difference between the ...
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There's no written policy (until now, I guess), and each mod has his or her quirks (so the discussion below is guaranteed to apply only if the handling moderator is yours truly). While you asked about "not constructive", let me be more ambitious and answer in the greatest generality. Before saying anything else, let me first say this:
Moderation on each ...
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More for my own sake than anything else. Integration duplicates tend to be quite hard to find due to the large amount of symbols in titles. Here is a short list of some famous integrals that pop up periodically
Integration integration
The Gaussian integral: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \dfrac{\sqrt \pi}{2}$. More proofs here.
The ...
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There ought to be an entry for the calculus / limit classic:
$$\lim_{n\to\infty} \left(1+\frac xn\right)^n = \exp x$$
I found these posts on it so far:
About $\lim \left(1+\frac {x}{n}\right)^n$
Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$
Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.
$\...
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Hypergeometric/Summation Identities summation
Rather than have these broken up among algebra-precalculus, proof by induction, combinatorics, etc. I am gathering them all in one place.
Faulhaber identities (sums of powers)
$\sum\limits_{k = 1}^n k = \frac{k(k+1)}{2}$ (triangle numbers)
What is the term for a factorial type operation, but with summation ...
7
Probability probability
"Two Children Puzzle / Boy Born on a Tuesday" and variants:
In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
New Two Children problem
Boy Born on a Tuesday - is it just a language trick?
A "liar paradox" variant: Multiple-choice question about the probability of a ...
7
Questions about [irreducible-polynomials] concerning generic methods:
Methods to see if a polynomial is irreducible
How to choose correct strategy for irreducibility testing in $\mathbb{Z}[X]$?
Checking irreducibility of polynomials over number fields
Techniques for checking irreducibility over the rationals
Does irreducibility in $\mathbb Q[X]$ always ...
5
A couple of analysis exercises that appear frequently:
prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
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I am adding this answer because the question came up again recently and, while much of what I wrote is a little redundant, there is an aspect of the culture of MSE which I think is worth discussing.
In general, a vote on the main site indicates that a post is poorly researched or of low quality. On Meta, votes should, for the most part, be interpreted ...
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A canonical answer would not be useful to this topic. Let's focus on the particular topic of questions asking about the minimization of a particular boolean expression, because, outside of this, we cannot anticipate, and have no interest in anticipating, what sorts of questions people might ask. I see two broad classes these questions might fall into:
Those ...
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