Intereting Posts

Arnol'd's trivium problem #68
Prime number theory and primes in a specific interval
What's the quickest way to see that the subset of a set of measure zero has measure zero?
Expected value of integrals of a gaussian process
How do you show that $f(x) = e^{-x^2}$ is in the Schwartz space $\mathcal{S}(\Bbb{R})$?
The vector space formed on C and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
Prove that the class number of $\mathbb{Z}$ is $1$
Conjectures (or intuitions) that turned out wrong in an interesting or useful way
Number $N>6$, such that $N-1$ and $N+1$ are primes and $N$ divides the sum of its divisors
How to draw a Mandelbrot Set with the connecting filaments visible?
Effect of the degree of a map $S^n\to M$ on lower homology groups
Proving all rational numbers including negatives are countable
isomorphism $\Bbb Q$ to $\Bbb Q \cap (0,1)$
Prove that if $({x+\sqrt{x^2+1}})({y+\sqrt{y^2+1}})=1$ then $x+y=0$
$a_n$ is bounded and decreasing

Given:

$0 \le a \le 1$

$0 \le b \le 1$

- If $ -3\left(x-\lfloor x \rfloor \right)^2+2(x-\lfloor x \rfloor )+a^2=0$ has no integral solution, then $a$ is
- How to solve for $x$ in $x(x^3+\sin x \cos x)-\sin^2 x =0$?
- simple/dumb logarithmic conversion question
- Problems with fake proofs of limit of sequences
- The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
- How to Expand Into Partial Fractions

Prove: $a + b – ab \le 1$

- Calculating Intersections of Lines and Algebraic Surfaces
- Fastest way to check if $x^y > y^x$?
- Proving :$\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1$
- Find the values of $m$ in the 2nd degree equation $(3m-2)x^2+2mx+3m=0$ so that it has only one root between -1 and 0
- Various proofs of Hardy's inequality
- Establishing the inequality at the heart of a popular sequence which converges to powers of $e$
- Ramsey Number proof: $R(3,3,3,3)\leq 4(R(3,3,3)-1) + 2$
- Nested solutions of a quadratic equation.
- Compound interest formula with regular deposits, solve for time
- How is $Ax + By = C$ the equation of a straight line?

Hint: in that interval,

$$(1-a)(1-b) \ge 0$$

$$ab-a-b+1=(a-1)(b-1)\ge 0$$ since $a-1\le0$ and $b-1\le 0$.

- Hausdorff metric and convex hull
- Why are rotational matrices not commutative?
- What use is the Yoneda lemma?
- Show that $5^n$ divides $F_{5^n}$.
- When can we use Fubini's Theorem?
- Prove the Countable additivity of Lebesgue Integral.
- A condition for a subgroup of a finitely generated free abelian group to have finite index
- Proving pointwise convergence of series of functions
- Is $\mathbb{Z} / \langle (x^2 + 1)^2 \rangle$ isomorphic to a familiar ring?
- Examples of patterns that eventually fail
- Number of zeros of the second derivative of composition of sigmoid-like functions
- Inequality with condition $x^2+y^2+z^2=1$.
- Theorem name or source: a (ruled) surface with a certain number of non-parallel lines is a plane
- Solution of Cauchy functional equation which has an antiderivative
- Smallest number with specific number of divisors