https://liberty.io/compute-the-double-sum-sum-n-m-0-n-neq-m-frac-1-n-left-m-2-n-2-right-f.htmlBuzz Spill Dailyen2026-09-04T01:25:06-04:00Compute the double sum $\sum_{n, m>0, n \neq m} \frac{1}{n\left(m^{2}-n^{2}\right)}=\frac{3}{4} \zeta(3)$https://liberty.io/definition-of-good-reduction.htmlBuzz Spill Dailyen2026-09-04T01:24:26-04:00Definition of "good reduction"https://liberty.io/symbol-for-the-set-of-integers-from-1-to-n-duplicate.htmlBuzz Spill Dailyen2026-09-04T01:14:06-04:00symbol for the set of integers from 1 to N [duplicate]https://liberty.io/an-open-ball-is-an-open-set.htmlBuzz Spill Dailyen2026-09-04T01:12:47-04:00An open ball is an open sethttps://liberty.io/finding-plane-equation-given-two-lines.htmlBuzz Spill Dailyen2026-09-04T01:09:26-04:00Finding plane equation given two lineshttps://liberty.io/could-someone-explain-me-what-is-a-clopen-set.htmlBuzz Spill Dailyen2026-09-04T01:00:20-04:00Could someone explain me what is a Clopen Sethttps://liberty.io/what-is-the-point-of-non-commutative-probability.htmlBuzz Spill Dailyen2026-09-04T01:00:13-04:00What is the point of non-commutative probability?https://liberty.io/solving-cos4-theta-cos3-theta-to-find-the-roots-of-8x-3-4x-2-4x-1-0.htmlBuzz Spill Dailyen2026-09-04T00:59:49-04:00Solving $\cos4\theta=\cos3\theta$ to find the roots of $8x^3+4x^2-4x-1=0$.https://liberty.io/what-are-the-common-abbreviation-for-minimum-in-equations.htmlBuzz Spill Dailyen2026-09-04T00:59:48-04:00What are the common abbreviation for minimum in equations?https://liberty.io/is-the-laplacian-a-vector-or-a-scalar.htmlBuzz Spill Dailyen2026-09-04T00:56:13-04:00Is the Laplacian a vector or a scalar?https://liberty.io/how-to-check-if-5-is-a-square-mod-701-without-a-calculator.htmlBuzz Spill Dailyen2026-09-04T00:55:34-04:00How to check if $5$ is a square $\mod 701$ without a calculatorhttps://liberty.io/difference-between-polynomial-functions-and-polynomials-and-why-these-.htmlBuzz Spill Dailyen2026-09-04T00:50:39-04:00Difference between polynomial functions and polynomials and why these two polynomial functions are equal?https://liberty.io/what-is-the-function-fsolve-in-python-doing-mathematically.htmlBuzz Spill Dailyen2026-09-04T00:45:29-04:00What is the function fsolve in python doing mathematically?https://liberty.io/constructibility-of-the-17-gon.htmlBuzz Spill Dailyen2026-09-04T00:43:17-04:00Constructibility of the 17-gonhttps://liberty.io/cosine-rule-to-find-a-side-of-a-triangle.htmlBuzz Spill Dailyen2026-09-04T00:29:28-04:00Cosine rule to find a side of a trianglehttps://liberty.io/drawing-a-phase-portrait-given-eigenvectors.htmlBuzz Spill Dailyen2026-09-04T00:25:50-04:00Drawing a phase portrait given Eigenvectorshttps://liberty.io/what-is-the-definition-of-2-5-2-5-factorial.htmlBuzz Spill Dailyen2026-09-04T00:22:06-04:00What is the definition of $2.5!$? (2.5 factorial)https://liberty.io/grandi-039-s-series-tends-to-1-2-but-why-is-this-considered-a-valid-su.htmlBuzz Spill Dailyen2026-09-04T00:14:39-04:00Grandi's Series; tends to $1/2$, but why is this considered a valid sum?https://liberty.io/how-can-i-show-that-a-function-is-non-decreasing.htmlBuzz Spill Dailyen2026-09-04T00:14:12-04:00How can I show that a function is non-decreasinghttps://liberty.io/questions-tagged-factoring.htmlBuzz Spill Dailyen2026-09-04T00:12:16-04:00Questions tagged [factoring] https://liberty.io/how-can-i-simply-prove-that-the-pearson-correlation-coefficient-is-bet.htmlBuzz Spill Dailyen2026-09-04T00:07:51-04:00How can I simply prove that the pearson correlation coefficient is between -1 and 1?https://liberty.io/optimisation-in-two-variables-second-order-conditions.htmlBuzz Spill Dailyen2026-09-04T00:01:53-04:00Optimisation in two variables - second order conditionshttps://liberty.io/why-is-it-that-0-5-0-5-equals-sin-pi-4.htmlBuzz Spill Dailyen2026-09-03T23:56:40-04:00Why is it that $0.5^{0.5}$ equals $\sin(\pi/4)$https://liberty.io/counting-the-number-of-real-roots-of-a-polynomial.htmlBuzz Spill Dailyen2026-09-03T23:49:41-04:00Counting the Number of Real Roots of A Polynomialhttps://liberty.io/what-is-the-modulus-of-a-matrix.htmlBuzz Spill Dailyen2026-09-03T23:48:58-04:00What is the Modulus of a Matrix?https://liberty.io/is-upper-hemi-continuity-and-upper-semi-continuity-the-same-thing-for-.htmlBuzz Spill Dailyen2026-09-03T23:47:46-04:00Is upper hemi-continuity and upper semi-continuity the same thing for set-valued function?https://liberty.io/confused-with-natural-logarithms.htmlBuzz Spill Dailyen2026-09-03T23:38:17-04:00Confused with natural logarithmshttps://liberty.io/spectrum-of-adjacency-matrix-of-complete-graph.htmlBuzz Spill Dailyen2026-09-03T23:28:20-04:00Spectrum of adjacency matrix of complete graphhttps://liberty.io/what-is-the-taylor-expansion-of-x-2-closed.htmlBuzz Spill Dailyen2026-09-03T23:22:07-04:00What is the Taylor Expansion of $x^2$ [closed]https://liberty.io/weird-integral-symbol-mathrel-int.htmlBuzz Spill Dailyen2026-09-03T23:18:49-04:00Weird integral symbol : $\mathrel{\int\!\!\!\!\!-}$https://liberty.io/formal-symbol-for-the-integer-division-operation.htmlBuzz Spill Dailyen2026-09-03T23:13:11-04:00Formal symbol for the integer division operationhttps://liberty.io/if-an-ideal-contains-the-multiplicative-identity-then-it-is-the-whole-.htmlBuzz Spill Dailyen2026-09-03T23:12:13-04:00If an ideal contains the multiplicative identity, then it is the whole ringhttps://liberty.io/taylor-series-of-frac-1-1-x-2.htmlBuzz Spill Dailyen2026-09-03T23:07:18-04:00Taylor series of $\frac 1 {1+x^2}$https://liberty.io/does-the-order-of-operations-matter-with-just-addition-and-subtraction.htmlBuzz Spill Dailyen2026-09-03T22:59:55-04:00Does the order of operations matter with just addition and subtraction?https://liberty.io/help-with-finding-the-directional-derivative-of-a-f-x-y-z-xy-xz-yz-at-.htmlBuzz Spill Dailyen2026-09-03T22:57:32-04:00Help with finding the directional derivative of a $f(x,y,z)=xy+xz+yz$ at a point and in the direction of a vectorhttps://liberty.io/team-balancing-score-normalisation-for-gamification.htmlBuzz Spill Dailyen2026-09-03T22:48:18-04:00Team Balancing / Score Normalisation for gamificationhttps://liberty.io/convective-derivative-vs-divergence-of-velocity.htmlBuzz Spill Dailyen2026-09-03T22:47:48-04:00Convective derivative vs Divergence of velocityhttps://liberty.io/a-ladder-leans-against-a-wall-but-the-problem-asks-how-long-is-the-lad.htmlBuzz Spill Dailyen2026-09-03T22:31:13-04:00A ladder leans against a wall, but the problem asks how long is the ladder.https://liberty.io/does-the-series-sum-frac-1-ln-3-k-converge-or-diverge.htmlBuzz Spill Dailyen2026-09-03T22:29:36-04:00Does the series $\sum \frac{1}{\ln^3(k)}$ converge or diverge?https://liberty.io/how-to-calculate-the-coordinates-of-a-triangle-039-s-orthocentre.htmlBuzz Spill Dailyen2026-09-03T22:22:41-04:00How to calculate the coordinates of a triangle's orthocentre?https://liberty.io/find-intersection-of-two-3d-lines.htmlBuzz Spill Dailyen2026-09-03T22:21:30-04:00Find intersection of two 3D lineshttps://liberty.io/determine-if-sum-n-1-infty-frac-1-nn-2-n-n-3-1-converges-or-diverges.htmlBuzz Spill Dailyen2026-09-03T22:15:55-04:00Determine if $\sum_{n=1}^{\infty}\frac{(-1)^nn^2+n}{n^3+1}$ converges or diverges.https://liberty.io/what-does-039-card-039-stands-for.htmlBuzz Spill Dailyen2026-09-03T22:07:40-04:00What does 'card' stands for?https://liberty.io/geometry-how-to-determine-if-two-lines-are-parallel-in-3d-based-on-coo.htmlBuzz Spill Dailyen2026-09-03T22:02:23-04:00Geometry: How to determine if two lines are parallel in 3D based on coordinates of 2 points on each line?https://liberty.io/show-that-measure-is-trivial.htmlBuzz Spill Dailyen2026-09-03T21:44:49-04:00Show that measure is trivialhttps://liberty.io/how-do-you-distinguish-the-difference-between-a-negative-sign-and-a-mi.htmlBuzz Spill Dailyen2026-09-03T21:44:02-04:00How do you distinguish the difference between a negative sign and a minus sign in Algebrahttps://liberty.io/proving-a-tautology-by-applying-a-chain-of-logical-identities.htmlBuzz Spill Dailyen2026-09-03T21:42:39-04:00Proving a tautology by applying a chain of logical identitieshttps://liberty.io/can-someone-explain-geometric-multiplicity.htmlBuzz Spill Dailyen2026-09-03T21:41:37-04:00Can someone explain geometric multiplicity?https://liberty.io/why-is-sqrt-2-sqrt-3-neq-sqrt-6.htmlBuzz Spill Dailyen2026-09-03T21:40:50-04:00Why is $\sqrt{-2} \sqrt{-3} \neq \sqrt{6}$?https://liberty.io/show-that-tan-pi-over-8-sqrt-2-1.htmlBuzz Spill Dailyen2026-09-03T21:29:32-04:00Show that $\tan {\pi \over 8} = \sqrt 2 - 1$https://liberty.io/in-general-what-does-the-location-of-the-rightmost-1-in-a-binary-numbe.htmlBuzz Spill Dailyen2026-09-03T21:27:43-04:00In general, what does the location of the rightmost “1” in a binary number tell you? Is it different for positive and for negative numbers?https://liberty.io/linear-bound-on-angles-in-an-euclidean-triangle.htmlBuzz Spill Dailyen2026-09-03T21:27:23-04:00Linear bound on angles in an euclidean triangle.https://liberty.io/about-algebraic-integer-and-algebraic-number.htmlBuzz Spill Dailyen2026-09-03T21:25:46-04:00About algebraic integer and algebraic numberhttps://liberty.io/pre-multiplying-and-post-multiplying-matrices-give-the-same-diagonal-e.htmlBuzz Spill Dailyen2026-09-03T21:13:44-04:00Pre-multiplying and post-multiplying matrices give the same diagonal elements?https://liberty.io/question-about-heart-shaped-graph.htmlBuzz Spill Dailyen2026-09-03T21:09:48-04:00Question about Heart-shaped-graphhttps://liberty.io/lagrangian-mechanics-derivatives.htmlBuzz Spill Dailyen2026-09-03T21:09:44-04:00Lagrangian Mechanics & Derivativeshttps://liberty.io/how-to-write-reciprocal-squared-function-shifted-right-by-3-and-down-b.htmlBuzz Spill Dailyen2026-09-03T21:05:57-04:00How to write reciprocal squared function shifted right by $3$ and down by $4$https://liberty.io/tail-sum-for-expectation.htmlBuzz Spill Dailyen2026-09-03T20:57:59-04:00Tail sum for expectationhttps://liberty.io/particular-solution-of-second-order-differential-equation.htmlBuzz Spill Dailyen2026-09-03T20:52:33-04:00Particular solution of second order differential equationhttps://liberty.io/quadratic-equations-and-factorized-form.htmlBuzz Spill Dailyen2026-09-03T20:46:57-04:00Quadratic Equations and factorized formhttps://liberty.io/an-infinite-dictionary-countably-infinite-or-uncountably-infinite.htmlBuzz Spill Dailyen2026-09-03T20:43:46-04:00An infinite dictionary: countably infinite or uncountably infinite?https://liberty.io/linear-combinations-of-sine-and-cosine.htmlBuzz Spill Dailyen2026-09-03T20:42:55-04:00Linear combinations of sine and cosinehttps://liberty.io/why-does-squaring-of-the-radius-of-a-circle-times-pi-give-us-the-area.htmlBuzz Spill Dailyen2026-09-03T20:38:31-04:00Why does squaring of the radius of a circle times pi give us the area?https://liberty.io/how-does-one-find-the-common-area-shared-between-two-polar-curves.htmlBuzz Spill Dailyen2026-09-03T20:24:22-04:00How does one find the common area shared between two polar curves?https://liberty.io/is-there-a-math-symbol-meaning-if-or-when.htmlBuzz Spill Dailyen2026-09-03T20:19:35-04:00Is there a math symbol meaning "If" or "when"?https://liberty.io/what-does-the-dot-over-x-or-y-mean.htmlBuzz Spill Dailyen2026-09-03T20:04:04-04:00What does the dot over $x$ or $y$ mean?https://liberty.io/prove-3-n-ge-n-3-by-induction.htmlBuzz Spill Dailyen2026-09-03T19:57:56-04:00Prove $3^n \ge n^3$ by inductionhttps://liberty.io/given-the-equation-x-sqrt-y-does-the-equation-represent-y-as-a-functio.htmlBuzz Spill Dailyen2026-09-03T19:46:15-04:00Given the equation $x = \sqrt{y}$, does the equation represent y as a function of x?https://liberty.io/how-to-understand-force-of-interest-in-simple-interest.htmlBuzz Spill Dailyen2026-09-03T19:45:26-04:00How to understand "force of interest" in simple interest?https://liberty.io/help-solving-a-differential-equation.htmlBuzz Spill Dailyen2026-09-03T19:37:00-04:00Help solving a differential equationhttps://liberty.io/equation-of-a-spherocylinder-capsule.htmlBuzz Spill Dailyen2026-09-03T19:36:44-04:00Equation of a spherocylinder/capsulehttps://liberty.io/not-getting-what-it-means-v-ai-bj-ck-for-some-vector-v.htmlBuzz Spill Dailyen2026-09-03T19:34:29-04:00Not getting what it means $v = ai + bj + ck$ for some vector $v$https://liberty.io/how-may-one-show-that-sin-x-sin-y-le-x-y-duplicate.htmlBuzz Spill Dailyen2026-09-03T19:33:36-04:00How may one show that $|\sin x-\sin y|\le |x-y|$? [duplicate]https://liberty.io/fractional-linear-transformations-and-their-matrix-form.htmlBuzz Spill Dailyen2026-09-03T19:29:03-04:00Fractional Linear Transformations and their matrix formhttps://liberty.io/proving-the-cauchy-schwarz-inequality-by-induction.htmlBuzz Spill Dailyen2026-09-03T19:25:40-04:00Proving the Cauchy-Schwarz inequality by inductionhttps://liberty.io/how-can-i-find-the-equation-of-a-parabola-only-given-it-039-s-x-interc.htmlBuzz Spill Dailyen2026-09-03T19:17:47-04:00How can I find the equation of a parabola only given it's x-intercepts?https://liberty.io/a-jacobi-elliptic-integral-with-cosine.htmlBuzz Spill Dailyen2026-09-03T19:11:00-04:00A Jacobi elliptic integral with cosinehttps://liberty.io/using-shell-method-find-the-volume-of-the-solid-generated-when-y-3-x-2.htmlBuzz Spill Dailyen2026-09-03T19:10:37-04:00Using shell method, find the volume of the solid generated when $y=3-x^2$ is revolved around x-axis from $y=0$ to $y=3$https://liberty.io/intuitive-explanation-of-duhamel-039-s-principle.htmlBuzz Spill Dailyen2026-09-03T18:58:39-04:00Intuitive explanation of Duhamel's principlehttps://liberty.io/translate-to-first-order-logic.htmlBuzz Spill Dailyen2026-09-03T18:53:30-04:00Translate to First Order Logichttps://liberty.io/variance-of-x-y.htmlBuzz Spill Dailyen2026-09-03T18:50:06-04:00Variance of X - Yhttps://liberty.io/ordinary-differential-equations-v-dx-dt.htmlBuzz Spill Dailyen2026-09-03T18:49:05-04:00Ordinary Differential Equations: v=dx/dthttps://liberty.io/how-the-product-of-two-integrals-is-iterated-integral-int-cdot-int-iin.htmlBuzz Spill Dailyen2026-09-03T18:47:24-04:00How the product of two integrals is iterated integral? $\int\cdot \int = \iint$https://liberty.io/simplify-sqrt-sqrt-3-5-sqrt-3-4.htmlBuzz Spill Dailyen2026-09-03T18:46:11-04:00Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.https://liberty.io/cauchy-schwarz-inequality-for-nonsymmetric-matrices.htmlBuzz Spill Dailyen2026-09-03T18:45:59-04:00Cauchy-Schwarz inequality for nonsymmetric matriceshttps://liberty.io/consistency-of-a-system-of-linear-equations-using-unknowns-in-the-matr.htmlBuzz Spill Dailyen2026-09-03T18:40:20-04:00Consistency of a System of linear equations using unknowns in the matrix formhttps://liberty.io/how-find-this-sum-sin-2-x-sin-2-2x-sin-2-3x-cdots-sin-2-nx.htmlBuzz Spill Dailyen2026-09-03T18:37:29-04:00How find this sum $\sin^2{x}+\sin^2{(2x)}+\sin^2{(3x)}+\cdots+\sin^2{(nx)}$https://liberty.io/change-of-polynomial-basis-exercise.htmlBuzz Spill Dailyen2026-09-03T18:26:53-04:00Change of polynomial basis exercisehttps://liberty.io/derivative-of-matrix-exponential-w-r-t-to-each-element-of-the-matrix.htmlBuzz Spill Dailyen2026-09-03T18:20:43-04:00Derivative of matrix exponential w.r.t. to each element of the matrixhttps://liberty.io/i-wonder-if-the-set-of-all-characteristic-function-on-a-set-a-is-simil.htmlBuzz Spill Dailyen2026-09-03T18:14:27-04:00I wonder if the set of all characteristic function on a set A is similar to its power set P(A) [duplicate]https://liberty.io/riemann-sheets-for-combined-roots.htmlBuzz Spill Dailyen2026-09-03T18:14:11-04:00Riemann sheets for combined rootshttps://liberty.io/proof-for-rational-roots.htmlBuzz Spill Dailyen2026-09-03T18:03:50-04:00Proof for rational rootshttps://liberty.io/derivative-of-operatorname-arcsec-3x.htmlBuzz Spill Dailyen2026-09-03T17:57:58-04:00Derivative of $\operatorname{arcsec}(3x)$https://liberty.io/prove-that-in-any-triangle-abc-cos-2a-cos-2b-cos-2c-geq-frac-3-4.htmlBuzz Spill Dailyen2026-09-03T17:56:16-04:00Prove that in any triangle $ABC$, $\cos^2A+\cos^2B+\cos^2C\geq\frac{3}{4}$https://liberty.io/can-i-subtract-infinity-from-infinity.htmlBuzz Spill Dailyen2026-09-03T17:55:32-04:00Can I subtract infinity from infinity?https://liberty.io/aaa-similarity-theorem.htmlBuzz Spill Dailyen2026-09-03T17:36:53-04:00AAA similarity Theorem.https://liberty.io/how-to-find-the-nth-term-in-the-following-sequence-1-1-2-2-4-4-8-8-16-.htmlBuzz Spill Dailyen2026-09-03T17:34:17-04:00How to find the nth term in the following sequence: $1,1,2,2,4,4,8,8,16,16$https://liberty.io/is-x-1-a-linear-function.htmlBuzz Spill Dailyen2026-09-03T17:28:59-04:00Is $x^{-1}$ a linear function?https://liberty.io/orthogonal-set-vs-orthogonal-basis.htmlBuzz Spill Dailyen2026-09-03T17:26:11-04:00Orthogonal set vs. orthogonal basishttps://liberty.io/why-are-all-non-prime-numbers-divisible-by-a-prime-number.htmlBuzz Spill Dailyen2026-09-03T17:14:21-04:00Why are all non-prime numbers divisible by a prime number?