Hottest Questions This Month

22 votes

6 answers

4k views

What is meant, exactly, by nonrepeating when talking about irrational numbers?

preferred_anon

16.3k

modified Apr 28 at 8:14

25 votes

5 answers

2k views

Are there are any inherent mathematical reasons some proofs are difficult?

logic reference-request soft-question intuition proof-theory

José Carlos Santos

397k

modified May 1 at 16:17

33 votes

2 answers

815 views

Does Fermat's Last Theorem imply $\sqrt{2} \not \in \mathbb{Q}$?

number-theory elementary-number-theory recreational-mathematics

Piquito

25.4k

answered May 4 at 2:00

11 votes

7 answers

722 views

The vertices of a tetrahedron lie on a sphere

soft-question euclidean-geometry symmetry spherical-geometry platonic-solids

Kyle Miller

17.4k

modified Apr 27 at 15:25

10 votes

7 answers

1k views

How to find the password space given several restrictions?

combinatorics permutations combinations

John Rehwinkel

1

modified May 6 at 15:05

17 votes

5 answers

435 views

Maclaurin series of $1- \cos^{2/3} x$ has all coefficients positive

calculus taylor-expansion

Claude Leibovici

213k

modified 2 days ago

26 votes

1 answer

738 views

Historical Mistake of Assuming Measurability

measure-theory math-history fake-proofs

温泽海

1,242

modified May 15 at 16:11

8 votes

3 answers

909 views

Why does a function has to be differentiable so many times to be considered smooth?

smooth-functions

Tanner Swett

8,885

answered Apr 26 at 18:36

12 votes

3 answers

387 views

Find all the functions $f:\mathbb{Z}^+ \to \mathbb{Z}^+$ such that $f(f(x)) = 15x-2f(x)+48$.

number-theory contest-math functional-equations

Sil

13.1k

modified May 12 at 7:22

4 votes

5 answers

635 views

On logical connector implies

logic

David

77k

modified May 7 at 6:50

7 votes

6 answers

594 views

What are some good, elementary and maybe also interesting proofs by induction?

induction examples-counterexamples

Bram28

91.3k

modified May 4 at 17:28

8 votes

3 answers

687 views

Differences between groups and rings when understood as categories

abstract-algebra category-theory

rschwieb

141k

modified May 11 at 15:33

11 votes

2 answers

431 views

What does a flattened Teserract look like?

3d solid-geometry

Mark McClure

28.3k

answered May 8 at 23:03

14 votes

2 answers

803 views

Better understanding dividing and forking

intuition model-theory

Primo Petri

3,869

modified Apr 28 at 22:59

20 votes

3 answers

624 views

Is $\frac{3^n+5^n+7^n}{15}$ only prime if $n$ is prime?

elementary-number-theory divisibility prime-factorization

Einar Rødland

8,202

modified May 3 at 22:21

7 votes

3 answers

351 views

Tough integral $\int_0^{ \pi }\frac{x^2(\pi-x)^2}{\sin^2 x} dx =6\pi\zeta(3) $

calculus integration complex-analysis definite-integrals

KStarGamer

3,092

modified Apr 28 at 16:56

13 votes

2 answers

894 views

What is the intuition behind simple Lie groups?

representation-theory lie-groups lie-algebras simple-groups

Youness EL KHARRAF

21

answered May 17 at 15:18

7 votes

2 answers

458 views

Can you, given any semigroup, define an identity element to make it a monoid

group-theory semigroups monoid

Bumblebee

16.3k

modified May 9 at 4:15

9 votes

4 answers

897 views

Mathematical Olympiad question (complex variable)

complex-analysis complex-numbers contest-math

River Li

22.5k

answered Apr 28 at 7:44

8 votes

2 answers

772 views

Exercise 6.A.17 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. I am worried if my solution is ok.

linear-algebra solution-verification normed-spaces inner-products

tchappy ha

6,079

answered May 10 at 4:26

13 votes

4 answers

564 views

why is $ 2 = \frac{5}{1+\frac{8}{4+\frac{11}{7 + \frac{14}{10 + \dots}}} } $

real-analysis continued-fractions

mick

12.9k

modified Apr 29 at 21:54

5 votes

4 answers

334 views

Explanation for a solution: Howard Anton, Elementary Linear Algebra

linear-algebra systems-of-equations

Doug M

6,203

modified Apr 26 at 19:49

12 votes

3 answers

227 views

Proving that out of all the possible n-gons that exist in the unit circle, the one with the maximum possible perimeter is the regular $n$-gon.

calculus convex-analysis analytic-geometry

robjohn♦

326k

modified May 1 at 21:03

7 votes

3 answers

441 views

$( \ X\to G \ , \ \star \ )$ is a group if $(\varphi \star \psi)(a) = \varphi(a) \star \psi(a)$

abstract-algebra group-theory functions

user21820

53.3k

modified May 18 at 15:20

8 votes

2 answers

410 views

Find a rectangular equation from a parametric equation. Why is my approach wrong?

calculus solution-verification parametric

dxiv

68.4k

modified May 14 at 6:25

11 votes

4 answers

237 views

Upper bound of $\sum_{n=1}^N |1-z^n|$ where $|z| \leq 1$

sequences-and-series complex-analysis complex-numbers power-series

G Cab

33.3k

answered May 12 at 17:15

3 votes

2 answers

493 views

10 good and 3 bad batteries are mixed and then 5 are chosen. What is the probability of the fifth one being dead given that the first 4 aren't?

probability combinatorics conditional-probability

JMoravitz

71.2k

modified May 10 at 16:31

11 votes

1 answer

470 views

Intuitive Explanation for Number of Dyck Paths Never Going Above Diagonal of a Rectangle

combinatorics intuition catalan-numbers

Mike Earnest

56.8k

answered May 18 at 21:35

5 votes

5 answers

156 views

Error in computing a limit

calculus limits

Robert Lee

5,020

modified May 12 at 9:47

9 votes

4 answers

521 views

Prove that $\sum_{1\le i<j\le n}\frac{x_ix_j}{(1-x_i)(1-x_j)} \le \frac{n(n-1)}{2(2n-1)^2}$

inequality summation

Hans

8,977

modified 5 hours ago

6 votes

3 answers

299 views

Find $x,y,z$ satisfying $x(y+z-x)=68-2x^2$, $y(z+x-y)=102-2y^2$, $z(x+y-z)=119-2z^2$

algebra-precalculus systems-of-equations problem-solving

user21820

53.3k

modified Apr 24 at 8:44

9 votes

3 answers

246 views

$\sum_{k=0}^\infty\frac{1}{k+1}\binom{3k+1}{k}\left(\frac{1}{2}\right)^{3k+2}$ converges to $\frac{3-\sqrt{5}}{2}$?

sequences-and-series convergence-divergence

Marco

2,708

modified 23 hours ago

8 votes

4 answers

312 views

Independent events or conditional probability?

probability

Vera

3,159

modified May 13 at 12:51

8 votes

3 answers

185 views

How can I integrate $\int_0^1 \bigl(1-x^n\bigr)^{2^n} \mathrm{d}x$? [closed]

real-analysis calculus limits uniform-convergence

River Li

22.5k

answered May 2 at 6:27

4 votes

3 answers

251 views

non linear differential equation that i cant solve

ordinary-differential-equations

David Billinghurst

11

modified May 9 at 11:21

7 votes

2 answers

340 views

Can you prove that these two series are equal?

real-analysis sequences-and-series analysis

Metin Ersin Arıcan

167

modified May 13 at 14:57

8 votes

3 answers

431 views

Connecting $\sqrt{i \sqrt{i \sqrt{i \sqrt{i \dots}}}}$ to an infinite process?

limits complex-numbers recreational-mathematics

Milten

5,721

modified May 18 at 15:42

18 votes

2 answers

420 views

A Proof with no words that $\sqrt{2+\sqrt{2+\sqrt{2+\cdots}}}=2$

real-analysis proof-explanation dynamical-systems nested-radicals proof-without-words

emacs drives me nuts

4,050

modified Apr 27 at 20:38

5 votes

4 answers

242 views

Simpler proof that $y^3[d^2y/dx^2]$ is a constant if $y^2=ax^2+bx+c$?

calculus derivatives alternative-proof chain-rule

user21820

53.3k

modified yesterday

11 votes

2 answers

225 views

Can $\sum_{n=1}^{k} \frac1{\sqrt{n}}$ be an integer for $k>1$?

number-theory

orangeskid

45.8k

modified May 17 at 19:55

11 votes

3 answers

132 views

Prove $\sum_{i,j:i<j} μ(E_{i} \cap E_{j} )=\infty$.

real-analysis measure-theory

Alex G.

8,126

answered yesterday

6 votes

2 answers

565 views

Is there a mistake in solving this limit?

limits limits-without-lhopital

Tyke

161

modified Apr 26 at 13:32

4 votes

3 answers

678 views

If someone wins 3000 rounds of a game out of 100000 numbered rounds of a game, what is the expected no. of last-3-digits of a round that they solved?

probability statistics random

awkward

12.8k

modified May 19 at 17:24

8 votes

1 answer

385 views

What is an instanton? (On a complex surface or a differentiable 4-manifold )

differential-geometry algebraic-geometry complex-geometry moduli-space

Warlock of Firetop Mountain

4,617

modified 2 days ago

8 votes

4 answers

231 views

How to evaluate $\int^{\infty}_0 \frac{x^{1010}}{(1 + x)^{2022}} dx$?

calculus integration definite-integrals improper-integrals

user581816

15

modified yesterday

7 votes

3 answers

137 views

Show that $p^k \mid \mid (x-y)$ iff $p^k \mid \mid (x^6-y^6)$.

number-theory

krewlpt

1,951

modified May 4 at 10:10

11 votes

2 answers

277 views

Yet another definition of uniform integrability. Is it equivalent to the classical definition by G.A. Hunt?

measure-theory

Oliver Díaz

26.2k

modified Apr 27 at 16:45

12 votes

3 answers

213 views

Proving $\left|\sin x\right|\leq\frac{(2m+1)!}{2^{4m}(m!)^2}\left[\binom{2m}{m} - \sum_{k=1}^{m} \frac{2}{4k^2-1} \binom{2m}{m+k} \cos(2kx) \right]$

inequality trigonometric-series

Sangchul Lee

140k

modified May 12 at 10:47

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