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Top Questions

22 votes
6 answers
4k views

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

25 votes
5 answers
2k views

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

33 votes
2 answers
815 views

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

11 votes
7 answers
722 views

The vertices of a tetrahedron lie on a sphere

10 votes
7 answers
1k views

How to find the password space given several restrictions?

17 votes
5 answers
435 views

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

26 votes
1 answer
738 views

Historical Mistake of Assuming Measurability

8 votes
3 answers
909 views

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

12 votes
3 answers
387 views

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

4 votes
5 answers
635 views

On logical connector implies

7 votes
6 answers
594 views

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

8 votes
3 answers
687 views

Differences between groups and rings when understood as categories

11 votes
2 answers
431 views

What does a flattened Teserract look like?

14 votes
2 answers
803 views

Better understanding dividing and forking

20 votes
3 answers
624 views

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

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) $

13 votes
2 answers
894 views

What is the intuition behind simple Lie groups?

7 votes
2 answers
458 views

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

9 votes
4 answers
897 views

Mathematical Olympiad question (complex variable)

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.

13 votes
4 answers
564 views

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

5 votes
4 answers
334 views

Explanation for a solution: Howard Anton, Elementary Linear Algebra

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.

7 votes
3 answers
441 views

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

8 votes
2 answers
410 views

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

11 votes
4 answers
237 views

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

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?

11 votes
1 answer
470 views

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

5 votes
5 answers
156 views

Error in computing a limit

9 votes
4 answers
521 views

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

6 votes
3 answers
299 views

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

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 $\frac{3-\sqrt{5}}{2}$?

8 votes
4 answers
312 views

Independent events or conditional probability?

8 votes
3 answers
185 views

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

4 votes
3 answers
251 views

non linear differential equation that i cant solve

7 votes
2 answers
340 views

Can you prove that these two series are equal?

8 votes
3 answers
431 views

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

18 votes
2 answers
420 views

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

5 votes
4 answers
242 views

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

11 votes
2 answers
225 views

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

11 votes
3 answers
132 views

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

6 votes
2 answers
565 views

Is there a mistake in solving this limit?

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?

8 votes
1 answer
385 views

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

8 votes
4 answers
231 views

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

7 votes
3 answers
137 views

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

11 votes
2 answers
277 views

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

12 votes
3 answers
213 views

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


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