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27 answers
512 votes
186k views
232 bookmarks
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
23 answers
442 votes
83k views
496 bookmarks
Proofs that every mathematician should know.
22 answers
428 votes
61k views
169 bookmarks
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
26 answers
246 votes
60k views
106 bookmarks
Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
2 answers
174 votes
66k views
139 bookmarks
Limit of $L^p$ norm
18 answers
173 votes
95k views
119 bookmarks
Taking Seats on a Plane
8 answers
170 votes
77k views
106 bookmarks
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
9 answers
166 votes
40k views
91 bookmarks
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
4 answers
163 votes
58k views
199 bookmarks
Overview of basic results about images and preimages
8 answers
162 votes
46k views
133 bookmarks
Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
19 answers
155 votes
18k views
49 bookmarks
What actually is a polynomial?
27 answers
116 votes
12k views
73 bookmarks
Unexpected examples of natural logarithm
3 answers
113 votes
8k views
93 bookmarks
Are all limits solvable without L'Hôpital Rule or Series Expansion
5 answers
109 votes
9k views
60 bookmarks
Fibonacci number that ends with 2014 zeros?
3 answers
105 votes
73k views
82 bookmarks
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
2 answers
98 votes
4k views
46 bookmarks
A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
15 answers
97 votes
41k views
72 bookmarks
If $(a_n)\subset[0,\infty)$ is non-increasing and $\sum a_n<\infty$, then $\lim{n a_n} = 0$
8 answers
87 votes
9k views
48 bookmarks
Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$
11 answers
85 votes
22k views
24 bookmarks
Expected number of unpecked chicks - NYT article
14 answers
74 votes
5k views
33 bookmarks
"Naturally occurring" non-Hausdorff spaces?
3 answers
67 votes
6k views
31 bookmarks
If I know the order of every element in a group, do I know the group?
2 answers
66 votes
8k views
54 bookmarks
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
5 answers
65 votes
5k views
38 bookmarks
Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
26 answers
64 votes
10k views
48 bookmarks
What are some mathematically interesting computations involving matrices?
10 answers
58 votes
9k views
18 bookmarks
Why does the discriminant in the Quadratic Formula reveal the number of real solutions?
2 answers
57 votes
36k views
59 bookmarks
Order of general- and special linear groups over finite fields.
5 answers
56 votes
41k views
72 bookmarks
$\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$.
3 answers
52 votes
11k views
38 bookmarks
$|G|>2$ implies $G$ has non trivial automorphism
3 answers
52 votes
11k views
21 bookmarks
Is it possible to place 26 points inside a rectangle that is 20 cm by 15 cm so that the distance between every pair of points is greater than 5 cm?
3 answers
52 votes
3k views
32 bookmarks
Why is the Galois Correspondence intuitively plausible?
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