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Enlightened

First to answer and accepted with score of 10 or more. This badge can be awarded multiple times.

Awarded 24794 times.

Prove that $\sum_{k=0}^n(-1)^k{n \choose k}\frac{1}{k+m+1}=\sum_{k=0}^m(-1)^k{m \choose k}\frac{1}{k+n+1}$.

Awarded Nov 11 at 14:37

Thomas Andrews

188k18 gold badges230 silver badges432 bronze badges

Every well-ordered set is isomorphic to a unique ordinal

Awarded Nov 11 at 4:09

Noah Schweber

265k22 gold badges398 silver badges683 bronze badges

Visualizing a basic triangle inequality in metric spaces

Awarded Nov 11 at 2:08

almost_okay

2,6611 gold badge3 silver badges12 bronze badges

In constructive math, does "$\mathbb R$ is the disjoint union of two non-empty sets" imply $\mathbb R = (-\infty,0] \cup (0,+\infty)$?

Awarded Nov 10 at 22:09

Gro-Tsen

6,56827 silver badges70 bronze badges

Prove that the square root of a positive integer is either an integer or irrational

Awarded Nov 10 at 6:36

fleablood

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A sequence based on Euler's totient function that always converges to prime numbers

Awarded Nov 10 at 0:19

Martin R

133k9 gold badges129 silver badges243 bronze badges

Do categories of bimodules have enough projectives?

Awarded Nov 9 at 5:35

Maxime Ramzi

45.3k4 gold badges40 silver badges115 bronze badges

What is a strictly convex function that is not strongly convex?

Awarded Nov 8 at 20:53

angryavian

94.3k7 gold badges77 silver badges147 bronze badges

Integral inequality with logarithm

Awarded Nov 8 at 20:53

Martin R

133k9 gold badges129 silver badges243 bronze badges

What is the "closest approximation" to fields by an equational variety?

Awarded Nov 8 at 13:32

Chris Grossack

43.4k5 gold badges59 silver badges111 bronze badges

Characterization of holomorphic function whose n-fold composition is the identity

Awarded Nov 7 at 20:24

Gerd

10.4k1 gold badge8 silver badges29 bronze badges

Visualization of Eratosthenes’ sieve

Awarded Nov 7 at 17:54

Asaf Karagila♦

408k48 gold badges651 silver badges1.1k bronze badges

Proving a set of automorphisms of a group is a group under composition

Awarded Nov 7 at 7:15

Mathematician 42

13.2k1 gold badge25 silver badges57 bronze badges

Are all natural numbers (except 1 and 2) part of at least one primitive pythagorean triplet?

Awarded Nov 5 at 19:55

Especially Lime

47.8k9 gold badges65 silver badges111 bronze badges

Can Peirce's Law be proven without contradiction?

Awarded Nov 5 at 16:45

hmakholm left over Monica

293k25 gold badges443 silver badges709 bronze badges

Gateaux derivatives is a linear continuous operator

Awarded Nov 5 at 11:40

leslie townes

9,3774 gold badges42 silver badges61 bronze badges

Are the letter choices in algebra meaningful?

Awarded Nov 5 at 7:46

badjohn

8,9142 gold badges20 silver badges36 bronze badges

Are there known natural problems of intermediate degrees of unsolvability?

Awarded Nov 5 at 3:42

Carl Mummert

87k13 gold badges179 silver badges326 bronze badges

If polynomial with rational number is injective on rationals then it is injective on reals?

Awarded Nov 5 at 0:22

Will Jagy

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Is the Pythagorean closure of $\mathbb Q$ equal to the field of constructible numbers?

Awarded Nov 4 at 17:42

Cam McLeman

6,4331 gold badge35 silver badges43 bronze badges

What exactly does a Möbius transformation do?

Awarded Nov 4 at 15:25

Conifold

12.2k3 gold badges36 silver badges64 bronze badges

Finding a degree-$d$ polynomial over $\Bbb C$ that has no multiple roots

Awarded Nov 3 at 15:00

Martin R

133k9 gold badges129 silver badges243 bronze badges

Definition of height of an ideal

Awarded Nov 2 at 23:10

Georges Elencwajg

158k14 gold badges323 silver badges504 bronze badges

How "close" can we get to a homeomorphism between non-homeomorphic surfaces?

Awarded Nov 2 at 19:19

Ben Steffan

10.8k5 gold badges20 silver badges58 bronze badges

Continuous mapping of Cantor Set to $[0,1]$

Awarded Nov 2 at 19:19

Eric Wofsey

344k28 gold badges487 silver badges705 bronze badges

Differentials on hyperelliptic curves

Awarded Nov 2 at 0:15

Viktor Vaughn

21.1k2 gold badges45 silver badges75 bronze badges

Perfect set vs perfect group

Awarded Oct 31 at 21:28

Martin Brandenburg

184k20 gold badges339 silver badges599 bronze badges

Product of Distinct Primitive roots

Awarded Oct 31 at 9:53

André Nicolas

516k47 gold badges589 silver badges1k bronze badges

How small can a set of the second category be?

Awarded Oct 30 at 20:54

spaceisdarkgreen

69.7k4 gold badges52 silver badges100 bronze badges

Closed form for $I_n = \int_0^{\pi} \frac{x \sin(nx)}{1 - \cos x}\, dx$

Awarded Oct 29 at 23:12

Afntu

4,2853 gold badges24 silver badges37 bronze badges

Closed-form solution to $\int_0^\infty (1 + \xi^2)^{n/4}\cos\left(\frac{m}{2}\tan^{-1}\xi\right)e^{-\alpha\xi^2}\mathrm{d}\xi\;$?

Awarded Oct 29 at 18:27

Gary

37.3k3 gold badges46 silver badges76 bronze badges

When does the difference between a vector bundle and the associated frame bundle matter?

Awarded Oct 29 at 18:27

geodude

8,4671 gold badge30 silver badges73 bronze badges

If $g$ is Riemann-integrable in a closed interval and $f$ is a increasing function in a closed interval, is $g\circ f$ Riemann-integrable?

Awarded Oct 29 at 13:35

Fimpellizzeri

23.4k2 gold badges28 silver badges44 bronze badges

Objections to power-set operation

Awarded Oct 29 at 13:35

Carl Mummert

87k13 gold badges179 silver badges326 bronze badges

Prove that $ AA^T=0\implies A = 0$

Awarded Oct 29 at 9:41

Timbuc

34.9k2 gold badges36 silver badges51 bronze badges

What do model theorists mean when they talk about set sizes?

Awarded Oct 29 at 5:41

Alex Kruckman

88.9k5 gold badges105 silver badges172 bronze badges

What is the formal and rigorous definition of a quantifier?

Awarded Oct 29 at 3:21

Noah Schweber

265k22 gold badges398 silver badges683 bronze badges

Does $2$ cancel multiplicatively in $\mathbf{ZF}$?

Awarded Oct 28 at 21:23

Alex Kruckman

88.9k5 gold badges105 silver badges172 bronze badges

Continuity of function mapping connected set to connected set

Awarded Oct 28 at 18:31

amWhy

211k198 gold badges285 silver badges506 bronze badges

How to show the even order derivatives of $f(x)=\big(1+\tan^{r}(x) \big)^{-1}$ are $0$?

Awarded Oct 28 at 14:28

Afntu

4,2853 gold badges24 silver badges37 bronze badges

Find rational roots of $x^4 - 4x^3 + 6x^2 - 4x + 1$

Awarded Oct 28 at 11:19

Sean Roberson

10.4k3 gold badges24 silver badges42 bronze badges

Show that $S$ is a group if and only if $aS=S=Sa$.

Awarded Oct 28 at 9:05

David

85.2k9 gold badges97 silver badges167 bronze badges

Median wealth after repeated iterations of multiplicative game?

Awarded Oct 27 at 21:26

btilly

3,2431 gold badge21 silver badges19 bronze badges

Reduction of Principal bundle's

Awarded Oct 27 at 6:12

Andreas Cap

22.6k1 gold badge24 silver badges43 bronze badges

Finding null space of matrix.

Awarded Oct 27 at 2:48

AAR

27.8k4 gold badges42 silver badges82 bronze badges

Is a topology determined by its converging nets?

Awarded Oct 26 at 20:19

Dermot Craddock

5,37914 silver badges34 bronze badges

Two squares in a circle intersecting at one point

Awarded Oct 25 at 14:11

Pranay

6,1141 gold badge15 silver badges30 bronze badges

should the 2 in L-2 norm notation be a subscript or superscript?

Awarded Oct 25 at 14:11

K B Dave

10.1k1 gold badge23 silver badges36 bronze badges

Prove that $2+2\sqrt{12n^2+1}$ is perfect square

Awarded Oct 25 at 14:11

S.C.B.

23.2k3 gold badges40 silver badges64 bronze badges

Clean proof of Baker-Campbell-Hausdorff Formula

Awarded Oct 25 at 10:38

md2perpe

30.4k2 gold badges27 silver badges61 bronze badges

Cantor set in base 3.

Awarded Oct 25 at 10:38

the8thone

4,2513 gold badges33 silver badges54 bronze badges

Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$

Awarded Oct 25 at 6:24

joriki

243k15 gold badges312 silver badges550 bronze badges

Show that the set of points where a real-valued continuous sequence of functions converges is $F_{\sigma\delta}$

Awarded Oct 24 at 19:17

Ishfaaq

10.3k3 gold badges35 silver badges62 bronze badges

Can the Fourier transform of a test function vanish on an interval?

Awarded Oct 24 at 8:27

Letac Gérard

4,0033 silver badges14 bronze badges

On the almost complex structure

Awarded Oct 24 at 8:27

Travis Willse

109k13 gold badges148 silver badges288 bronze badges

Proof that group of even order contains element of order 2

Awarded Oct 24 at 8:27

Anurag A

42.5k1 gold badge41 silver badges74 bronze badges

In what way is the structure of the Turing degrees "extremely complicated"?

Awarded Oct 24 at 8:27

Noah Schweber

265k22 gold badges398 silver badges683 bronze badges

Equivalence of two definitions of a Frobenius group?

Awarded Oct 23 at 23:05

Lorban

1,73112 silver badges26 bronze badges

Minkowski inequality of infinite sum

Awarded Oct 23 at 16:02

kobe

43.4k2 gold badges43 silver badges73 bronze badges

Why is the sample mean a random variable?

Awarded Oct 23 at 6:52

Qiaochu Yuan

477k55 gold badges1.1k silver badges1.5k bronze badges

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