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Prove that $\int_0^1 |f(x) - g(x)| dx \leq \frac{1}{2}$ for two increasing functions in a $1 \times 1$ square

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Chuqing

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Formula for the number of divisors of an integer

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Brummi

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Sudoku: Maximal minimum number of starting clues

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hexomino

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Prove or disprove the conjecture: $\frac{a^3}{12}\ge\int_{0}^{a}|F(x)-\frac{1}{2}x|^2dx$

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math110

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Existence of finite non-associative fields

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How to remember Stolz Angle correctly

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yoyostein

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Real valued function, $M$, $s_n \rightarrow s; |f(s_n)| \le M$ for $s$ in open $U$. (Problem from Gamelin and Greene)

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fleablood

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Determining whether $A\subset X = \left\{0,1,\ldots,n\right\}$ can be written as $A=B+C$

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Dilemian

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What is $\lim_n \sqrt[n]{1+\cos(n)}$?

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Bruno Stonek

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Is there a theory stronger than ZFC in consistency but does not prove its consistency?

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Noiril

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Is $f(x)=\sum_{n=1}^\infty \frac{\sin(nx)}{\sqrt{n}}$ differentiable on $(0,2\pi)$?

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Riemann

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Help with $\int_{0}^{\pi /4} x^3 (\sqrt{\tan (x)} + \sqrt{\cot (x)}) dx$

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Md Iqbal Kotha

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Evaluating the definite integral of an absolute value involving trigonometric functions

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seljuk

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In how many ways can a permutation cycle be decomposed as a product of transpositions?

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Jan Hrcek

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Can there be a continuous function with infinite derivative everywhere?

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pie

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Subfields of the $p$-adic numbers

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Alphonse

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Subring which is not an ideal?

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Ystar

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Geometric interpretation of linear programming dual

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Daishisan

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Generating a random derangement

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Mythio

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How far can an infinite number of unit length planks bridge a right-angled gap?

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The Guy with The Hat

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Is the Collatz map algorithmically decidable?

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Vincent

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What square is expected $\mod n$?

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Dair

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Not all finitely-presented groups are fundamental groups of closed 3-manifolds

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Seirios

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Is an interpretation just a homomorphism between theories?

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R. Burton

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What's wrong with my understanding of the Freyd-Mitchell Embedding Theorem?

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tcamps

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Integral $ I=\int_{0}^{\infty}\frac{\cosh\!\big(\tfrac{\pi x}{2}\big)}{\big(1+2\cosh(\pi x)\big)\,(1+x^2)}\,dx. $

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Federico

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Collatz-type problems with known divergent trajectories

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Wojowu

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What is the correct definition of a limit point in real analysis?

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user1540346

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Evaluate: $4^9-\binom{8}{1}4^8+\binom{7}{2}4^7-\binom{6}{3}4^6+\binom{5}{4}4^5$

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Maverick

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Developing solution for electrodynamics problem

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generic properties

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Why Is the Dual Basis Mathematically Unavoidable?

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Aurora Borealis

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Computing class group of $\mathbb Q(\sqrt{6})$

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James

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Every uniformly continuous real function has at most linear growth at infinity

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M.H

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Is this formula for cosine correct? (And is it significant) [closed]

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Val0

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If M+N and M$\cap$N are finitely generated modules, so are M and N.

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user66733

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Big picture behind how to use KKT conditions for constrained optimization

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user25004

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Is the transfer principle useless?

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Super Cool Guy

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Problem about ratio between circumradius and inradius

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Martin Samanez

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Do division rings have algebraic closures?

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Gérard Lang

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Can chess moves be identified as a meaningful algebraic structure?

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Clemens Bartholdy

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Formula for $\sin(\pi/n)$ with $n$ a positive integer [closed]

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GSA_1

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The longest distance travelled by an ant on the sides of a cube.

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User

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Closed-form of $\int_0^1 \operatorname{Li}_3\left(1-x^2\right) dx$

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user153012

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solutions of $a+b=c^2 , a^2+c^2=b^2$ ; $a,b,c$ are natural numbers

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Avi

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Proof of existence of square root of unitary and symmetric matrix

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user1111261

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Non-recursive, explicit rational sequence that converges to $\sqrt{2}$

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Francesco Bollini

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Why Does Tao Use Inductive Language When Giving Recursive Definitions?

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Federico Tecleme

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Nontrivial integral representation for Euler's number $e$.

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Alma Arjuna

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Uncountably many sets of natural numbers with finite intersections [duplicate]

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user57041

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integrate $\int \frac{1}{e^{x}+e^{ax}+e^{a^{2}x}} \, dx$

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Calimops

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Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?

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Crowbar Jones

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What are some good sources to learn about real analytic manifolds?

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user42388

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Diagonalizing the Laplace operator

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agb

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Partitioning $\{1,4,9,\cdots,500^2\}$ into subsets with equal sums

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megidderp

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Prove $\frac{a^2+b^2+c^2}{ab+bc+ca} + 8\frac{abc}{(a+b)(b+c)(c+a)} \ge 2$

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user169301

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What is the expected value of the number of factors of a number?

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Kyan Cheung

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Does every (possibly infinite dimensional) vector space have an orthogonal Hamel basis?

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semilocallysimplyconnected

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Evaluating trisections of $\zeta(3)$: $\sum_{k=0}^\infty\frac1{(3k+1)^3}$

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Pranav Arora

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Regular in codimension 1

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Hock

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Function which derivative at $0$ is $1$ but is not monotonic increasing

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Trucker

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