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Mathematics

Enlightened

 Enlightened
First to answer and accepted with score of 10 or more. This badge can be awarded multiple times.
Awarded 24794 times.
Does "the preimage of a closed interval is a finite union of closed intervals" imply $f:\mathbb{R}\to\mathbb{R}$ is continuous?
Awarded 9 hours ago
Prove regular language closed under min and max
Awarded 13 hours ago
Prove $\int_0^af(x)\mathrm dx\ge a\int_0^1f(x)\mathrm dx$ for decreasing function
Awarded yesterday
A subset of a rectangle that 'blocks' every curve that goes from right to left must connect upper and lower sides
Awarded 2 days ago
Sufficient / necessary conditions for $g \circ f$ being injective, surjective or bijective
Awarded 2 days ago
What comes after diagram chasing?
Awarded Nov 27 at 20:56
Analytic Applications of Stone-Čech compactification
Awarded Nov 27 at 18:47
How far can an infinite number of unit length planks bridge a right-angled gap?
Awarded Nov 26 at 21:33
Is there a closed form for the linear operator $T$ such that $T(x^n) =f(n)x^{n-1}$?
Awarded Nov 26 at 20:57
Why is the trace of a matrix important?
Awarded Nov 26 at 13:14
Show that $\int_0^{\infty}\frac{\operatorname{Li}_s(-x)}{x^{\alpha+1}}\mathrm dx=-\frac1{\alpha^s}\frac{\pi}{\sin(\pi \alpha)}$
Awarded Nov 26 at 2:17
An alternative proof that the reals are uncountably infinite.
Awarded Nov 25 at 21:05
An open subset of a manifold is a manifold
Awarded Nov 25 at 21:05
Are $C^\infty$ exotic spheres $C^k$ exotic?
Awarded Nov 25 at 15:51
Evaluate: $4^9-\binom{8}{1}4^8+\binom{7}{2}4^7-\binom{6}{3}4^6+\binom{5}{4}4^5$
Awarded Nov 25 at 9:26
On Ramanujan's fastest series.
Awarded Nov 24 at 13:25
Solve recurrence for strings that do not contain the substring 101
Awarded Nov 23 at 17:18
Are one-point sets always compact in any topological spaces?
Awarded Nov 23 at 13:12
Find the number of subsets $A$ of $S= \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$ such that: $x\in A\wedge 2x\in S\implies 2x \in A$
Awarded Nov 23 at 13:12
What are the subobjects of a manifold?
Awarded Nov 22 at 12:36
Intuitive explanation of why the modified Gram-Schmidt is more stable than the classical one?
Awarded Nov 22 at 6:57
Are ceiling and floor elementary functions?
Awarded Nov 21 at 20:18
Can a function be differentiable at only isolated points?
Awarded Nov 21 at 15:56
How would I show that $\sin$ is continuous?
Awarded Nov 21 at 13:17
Examples of countable non-commutative division rings
Awarded Nov 21 at 13:17
$\int_0^{\infty}\text{Ai}^4(x)dx = \ln(3)/24 \pi^2$
Awarded Nov 20 at 22:27
Does the Laplacian and gradient commute?
Awarded Nov 20 at 22:27
Is this formula for cosine correct? (And is it significant)
Awarded Nov 20 at 15:30
Rules of imaginary numbers
Awarded Nov 20 at 15:30
Commutator of a group
Awarded Nov 20 at 12:07
How does the coefficient ring influence the Euler characteristic?
Awarded Nov 20 at 3:03
Why is $\mathfrak{m}/\mathfrak{m}^{2}$ the cotangent space to a variety?
Awarded Nov 19 at 23:41
Do division rings have algebraic closures?
Awarded Nov 19 at 23:41
Why is Erdős–Szekeres theorem sharp?
Awarded Nov 19 at 15:41
Non-recursive, explicit rational sequence that converges to $\sqrt{2}$
Awarded Nov 18 at 23:02
Why does this method work some of the time (but only some?)
Awarded Nov 18 at 23:02
How to evaluate $\int_{0}^{1}\frac{\arctan x}{1+x^{2}}\ln\left ( \frac{1+x^{2}}{1+x} \right )\mathrm{d}x$
Awarded Nov 18 at 23:02
Request for a proof of the following continued-fraction identity
Awarded Nov 18 at 18:05
Nontrivial integral representations for $e$
Awarded Nov 18 at 17:37
Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?
Awarded Nov 18 at 17:37
Support of a measure and set where it is concentrated
Awarded Nov 17 at 22:46
On $\int_0^1\frac{a+2x}{\sqrt{x(1-x)(a+x)(1+a+x)}}dx=\pi$
Awarded Nov 17 at 19:10
Any ring is integral over the subring of invariants under a finite group action
Awarded Nov 17 at 19:10
continuously averaging a stream of numbers
Awarded Nov 17 at 11:21
How to remove duplicate roots from a polynomial?
Awarded Nov 17 at 3:48
Help understanding the inclusion map
Awarded Nov 17 at 1:53
Is there a tame proof of "No anti-knots?"
Awarded Nov 17 at 1:53
Does every (possibly infinite dimensional) vector space have an orthogonal Hamel basis?
Awarded Nov 16 at 18:19
What's the difference between "function" and "relation" in logic?
Awarded Nov 16 at 16:39
Proving $\frac{1}{\cos^2\frac{\pi}{7}}+ \frac {1}{\cos^2\frac {2\pi}{7}}+\frac {1}{\cos^2\frac {3\pi}{7}} = 24$
Awarded Nov 15 at 19:51
Why is this angle always less than $49°$?
Awarded Nov 14 at 22:53
No well-ordered set is isomorphic to any of its initial segments
Awarded Nov 14 at 17:30
"Numerical results" from category theory
Awarded Nov 14 at 10:41
Definitions of Flat Connections
Awarded Nov 14 at 6:33
$ST$ and $TS$ have the same eigenvalues.
Awarded Nov 13 at 15:28
Do finite additivity and countable subadditivity imply countable additivity?
Awarded Nov 13 at 12:57
Continuous extensions of GCD to $\Bbb R^{+}\!\!\times \Bbb R^{+}\!$ still commutative and distributive
Awarded Nov 12 at 17:00
Fibonacci / Lucas Numbers Relationship: $F_{2n} = F_n L_n$
Awarded Nov 12 at 8:48
Is there an analog of Markov's Inequality (or Chebychev) for Medians?
Awarded Nov 11 at 18:41
What's are all the prime elements in Gaussian integers $\mathbb{Z}[i]$
Awarded Nov 11 at 17:36
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