https://liberty.io/show-that-if-h-and-k-are-subgroups-of-one-abelian-group-g-then-g-1-hk-.htmlBuzz Spill Dailyen2026-08-27T17:41:25-04:00Show that if $H$ and $K$ are subgroups of one abelian group $G$, then $G_1=\{hk\mid h\in H\text{ and }k\in K\}$ is a subgroup of $G$ [duplicate]https://liberty.io/fitch-system-or-alternatives.htmlBuzz Spill Dailyen2026-08-27T17:34:09-04:00Fitch system, or alternatives?https://liberty.io/icosahedral-symmetry-as-permutation-group.htmlBuzz Spill Dailyen2026-08-27T17:29:04-04:00Icosahedral symmetry as permutation grouphttps://liberty.io/when-to-use-the-contrapositive-to-prove-a-statment.htmlBuzz Spill Dailyen2026-08-27T17:27:11-04:00When to use the contrapositive to prove a statmenthttps://liberty.io/is-my-understanding-of-antisymmetric-and-symmetric-relations-correct.htmlBuzz Spill Dailyen2026-08-27T17:18:12-04:00Is my understanding of antisymmetric and symmetric relations correct?https://liberty.io/using-method-of-moments-on-binomial-distribution-closed.htmlBuzz Spill Dailyen2026-08-27T17:17:09-04:00Using method of moments on binomial distribution [closed]https://liberty.io/recurrence-relation-merge-sort.htmlBuzz Spill Dailyen2026-08-27T17:11:30-04:00Recurrence Relation - Merge Sorthttps://liberty.io/integral-from-infinity-to-infinity.htmlBuzz Spill Dailyen2026-08-27T17:11:11-04:00Integral from infinity to infinityhttps://liberty.io/a-parallelogram-and-a-circle.htmlBuzz Spill Dailyen2026-08-27T16:58:59-04:00A parallelogram and a circlehttps://liberty.io/why-is-two-the-only-even-number-that-is-prime.htmlBuzz Spill Dailyen2026-08-27T16:58:54-04:00Why is two the only even number that is prime?https://liberty.io/relaxed-menage-problem-sitting-arrangement-for-couples.htmlBuzz Spill Dailyen2026-08-27T16:55:17-04:00Relaxed Menage Problem - sitting arrangement for coupleshttps://liberty.io/in-classical-logic-why-is-p-rightarrow-q-true-if-p-is-false-and-q-is-t.htmlBuzz Spill Dailyen2026-08-27T16:50:59-04:00In classical logic, why is $(p\Rightarrow q)$ True if $p$ is False and $q$ is True?https://liberty.io/how-do-you-rotate-a-vector-by-a-unit-quaternion.htmlBuzz Spill Dailyen2026-08-27T16:48:09-04:00How do you rotate a vector by a unit quaternion?https://liberty.io/finding-limit-of-multivariable-function-using-the-squeeze-theorem.htmlBuzz Spill Dailyen2026-08-27T16:38:44-04:00Finding limit of multivariable function using the squeeze theoremhttps://liberty.io/proof-of-the-continuous-image-of-a-connected-set-is-connected.htmlBuzz Spill Dailyen2026-08-27T16:38:21-04:00Proof of "the continuous image of a connected set is connected"https://liberty.io/proving-the-inverse-if-any-of-a-lower-triangular-matrix-is-lower-trian.htmlBuzz Spill Dailyen2026-08-27T16:15:36-04:00Proving the inverse (if any) of a lower triangular matrix is lower triangularhttps://liberty.io/factorising-fourth-power-polynomial-with-5-terms-duplicate.htmlBuzz Spill Dailyen2026-08-27T16:05:11-04:00Factorising fourth power polynomial with 5 terms [duplicate]https://liberty.io/what-does-the-ln-or-1n-mean-in-this-equation.htmlBuzz Spill Dailyen2026-08-27T15:54:57-04:00What does the ln or 1n mean in this equation?https://liberty.io/calculate-sides-of-right-triangle-with-hypotenuse-and-area-or-perimete.htmlBuzz Spill Dailyen2026-08-27T15:53:12-04:00Calculate sides of right triangle with hypotenuse and area or perimeterhttps://liberty.io/what-does-ll-mean.htmlBuzz Spill Dailyen2026-08-27T15:50:57-04:00What does $\ll$ mean?https://liberty.io/notation-for-repeated-division.htmlBuzz Spill Dailyen2026-08-27T15:47:35-04:00Notation for repeated divisionhttps://liberty.io/finding-formula-for-nth-partial-sum.htmlBuzz Spill Dailyen2026-08-27T15:41:06-04:00Finding formula for nth partial sumhttps://liberty.io/related-rates-question-a-man-starts-walking-north-at-4-ft-s-from-a-poi.htmlBuzz Spill Dailyen2026-08-27T15:29:16-04:00Related Rates question: A man starts walking north at 4 ft/s from a point P. Five minutes later a woman startshttps://liberty.io/checking-for-validity-using-truth-table-shortcut.htmlBuzz Spill Dailyen2026-08-27T15:28:09-04:00Checking for validity using truth table (shortcut)https://liberty.io/what-is-category-theory-useful-for.htmlBuzz Spill Dailyen2026-08-27T15:11:46-04:00What is category theory useful for?https://liberty.io/integration-of-fundamental-solution-of-laplace-039-s-equation.htmlBuzz Spill Dailyen2026-08-27T15:03:25-04:00Integration of Fundamental Solution of Laplace's equation.https://liberty.io/how-to-find-the-derivative-of-the-function-f-x-2x-3-4-x-2-x-1-5.htmlBuzz Spill Dailyen2026-08-27T15:01:23-04:00How to find the derivative of the function $f(x) = (2x-3)^4 (x^2 + x + 1)^5$?https://liberty.io/what-is-a-smooth-surface.htmlBuzz Spill Dailyen2026-08-27T14:49:46-04:00What is a smooth surface?https://liberty.io/what-exactly-does-it-mean-for-a-function-to-be-well-behaved.htmlBuzz Spill Dailyen2026-08-27T14:49:28-04:00What exactly does it mean for a function to be "well-behaved"?https://liberty.io/what-039-s-the-correct-definition-of-conjugate-and-do-we-identify-them.htmlBuzz Spill Dailyen2026-08-27T14:41:26-04:00What's the correct definition of "conjugate", and do we identify them?https://liberty.io/trace-norm-properties.htmlBuzz Spill Dailyen2026-08-27T14:40:27-04:00Trace Norm propertieshttps://liberty.io/sd-of-a-bernoulli-trial.htmlBuzz Spill Dailyen2026-08-27T14:29:43-04:00SD of a bernoulli trial?https://liberty.io/euclidean-norm-and-matrix-question.htmlBuzz Spill Dailyen2026-08-27T14:28:32-04:00Euclidean norm and matrix questionhttps://liberty.io/notation-is-a-monotonic-function-of.htmlBuzz Spill Dailyen2026-08-27T14:22:10-04:00Notation: "is a monotonic function of"?https://liberty.io/trigonometric-expression-for-1-cos-alpha-cos-2-alpha-cdots-cos-n-alpha.htmlBuzz Spill Dailyen2026-08-27T14:12:14-04:00Trigonometric Expression for $1 + \cos \alpha + \cos 2\alpha + \cdots + \cos n \alpha$ using complex numbershttps://liberty.io/how-frac-1-x-is-integrable-if-it-is-not-a-continuous-function.htmlBuzz Spill Dailyen2026-08-27T14:04:28-04:00How $\frac{1}{x}$ is integrable if it is not a continuous functionhttps://liberty.io/ackermann-039-s-function-is-mu-recursive.htmlBuzz Spill Dailyen2026-08-27T13:46:41-04:00Ackermann's function is $\mu$-recursivehttps://liberty.io/prove-that-cot-2-pi-7-cot-2-2-pi-7-cot-2-3-pi-7-5.htmlBuzz Spill Dailyen2026-08-27T13:43:09-04:00Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$https://liberty.io/definition-of-degree-matrix-of-directed-graph.htmlBuzz Spill Dailyen2026-08-27T13:35:35-04:00definition of degree matrix of directed graph?https://liberty.io/how-many-axis-of-symmetry-of-the-cube-are-there.htmlBuzz Spill Dailyen2026-08-27T13:31:01-04:00How many axis of symmetry of the cube are there?https://liberty.io/sum-of-divergent-and-convergent-series.htmlBuzz Spill Dailyen2026-08-27T13:30:28-04:00Sum of Divergent and Convergent Serieshttps://liberty.io/what-is-the-meaning-of-the-term-distance-preserving.htmlBuzz Spill Dailyen2026-08-27T13:24:22-04:00What is the meaning of the term "distance-preserving"?https://liberty.io/what-is-the-use-of-calculus.htmlBuzz Spill Dailyen2026-08-27T13:15:38-04:00What is the use of Calculus?https://liberty.io/real-world-examples-of-continuous-uniform-distribution-on-0-1.htmlBuzz Spill Dailyen2026-08-27T13:14:09-04:00Real world examples of continuous uniform distribution on [0,1]https://liberty.io/on-the-proof-of-fleury-039-s-algorithm-question-2.htmlBuzz Spill Dailyen2026-08-27T13:09:57-04:00On the proof of Fleury's algorithm. (Question 2)https://liberty.io/what-does-the-term-arbitrary-number-mean-in-math.htmlBuzz Spill Dailyen2026-08-27T13:00:54-04:00What does the term "arbitrary number" mean in math?https://liberty.io/computing-t-beta-notation.htmlBuzz Spill Dailyen2026-08-27T12:59:00-04:00Computing $[T]_\beta$ notationhttps://liberty.io/trisecting-angles-which-can-be-trisected.htmlBuzz Spill Dailyen2026-08-27T12:52:05-04:00Trisecting angles which can be trisectedhttps://liberty.io/what-is-the-value-of-xyz.htmlBuzz Spill Dailyen2026-08-27T12:47:16-04:00What is the value of xyz?https://liberty.io/dice-game-probability-theory.htmlBuzz Spill Dailyen2026-08-27T12:42:53-04:00Dice Game - Probability Theoryhttps://liberty.io/what-is-a-function.htmlBuzz Spill Dailyen2026-08-27T12:40:31-04:00What is a function?https://liberty.io/sum-of-frac-1-n-2-for-n-1-2-3-duplicate.htmlBuzz Spill Dailyen2026-08-27T12:38:55-04:00Sum of $\frac{1}{n^{2}}$ for $n = 1 ,2 ,3, ...$? [duplicate]https://liberty.io/prove-two-angles-add-up-to-90-degrees.htmlBuzz Spill Dailyen2026-08-27T12:38:54-04:00Prove two angles add up to 90 degreeshttps://liberty.io/the-antiderivative-of-sin-1-x.htmlBuzz Spill Dailyen2026-08-27T12:36:47-04:00The antiderivative of $\sin(1/x)$https://liberty.io/why-can-we-use-geometric-proofs-in-algebra.htmlBuzz Spill Dailyen2026-08-27T12:35:27-04:00Why can we use geometric proofs in algebra?https://liberty.io/understanding-the-definition-of-a-splitting-field.htmlBuzz Spill Dailyen2026-08-27T12:30:17-04:00Understanding the definition of a splitting fieldhttps://liberty.io/new-pattern-question-2-7-26-101-400-closed.htmlBuzz Spill Dailyen2026-08-27T12:21:11-04:00New pattern question: $2, 7, 26, 101, 400$ [closed]https://liberty.io/calculus-question-with-circle-and-string-tracing-an-area.htmlBuzz Spill Dailyen2026-08-27T12:19:56-04:00Calculus question with circle, and string tracing an areahttps://liberty.io/find-an-equation-of-the-line-tangent-to-the-graph-of-at-the-point-wher.htmlBuzz Spill Dailyen2026-08-27T12:14:24-04:00Find an equation of the line tangent to the graph of 𝐶 at the point where 𝑡=1https://liberty.io/how-to-translate-a-vector-and-then-rotate-by-a-point.htmlBuzz Spill Dailyen2026-08-27T12:13:14-04:00How to translate a vector and then rotate by a pointhttps://liberty.io/minimum-velocity.htmlBuzz Spill Dailyen2026-08-27T12:12:13-04:00Minimum velocityhttps://liberty.io/complex-analysis-liouville-039-s-theorem-application-and-polynomial-de.htmlBuzz Spill Dailyen2026-08-27T12:03:30-04:00Complex Analysis - Liouville's Theorem application and polynomial degreehttps://liberty.io/number-of-possible-combinations-of-the-enigma-machine-plugboard.htmlBuzz Spill Dailyen2026-08-27T11:39:23-04:00Number of possible combinations of the Enigma machine plugboardhttps://liberty.io/projection-of-triangle-in-3d-to-2d-and-reverse.htmlBuzz Spill Dailyen2026-08-27T11:35:53-04:00Projection of triangle in 3D to 2D, and reversehttps://liberty.io/finding-the-dihedral-angle-of-a-octahedron.htmlBuzz Spill Dailyen2026-08-27T11:27:38-04:00Finding the dihedral angle of a octahedronhttps://liberty.io/questions-about-aleph-aleph-null.htmlBuzz Spill Dailyen2026-08-27T11:19:17-04:00Questions about Aleph-Aleph-Nullhttps://liberty.io/integer-expression.htmlBuzz Spill Dailyen2026-08-27T11:15:32-04:00Integer expressionhttps://liberty.io/when-is-mathbb-b-mathbb-x-compact.htmlBuzz Spill Dailyen2026-08-27T11:14:20-04:00When is $\mathbb{B}(\mathbb{X})$ compact?https://liberty.io/what-does-s-1-2-3-mean.htmlBuzz Spill Dailyen2026-08-27T11:09:34-04:00What does $S = \{1,2,3 \}^*$ mean?https://liberty.io/sin-6-6-or-sin-6-6.htmlBuzz Spill Dailyen2026-08-27T11:07:06-04:00Sin (6°)=6 or sin(6)=6https://liberty.io/cryptography-solve-x-2-equiv-331-pmod-385-using-modular-arithmetic.htmlBuzz Spill Dailyen2026-08-27T11:05:42-04:00Cryptography: Solve $x^2 \equiv 331 \pmod{385}$ using modular arithmetichttps://liberty.io/angle-between-two-surfaces.htmlBuzz Spill Dailyen2026-08-27T10:55:11-04:00Angle between two surfaceshttps://liberty.io/when-simplifying-sin-arctan-x-why-is-negative-x-not-considered.htmlBuzz Spill Dailyen2026-08-27T10:54:34-04:00When simplifying $\sin(\arctan(x))$, why is negative $x$ not considered?https://liberty.io/can-i-solve-this-differential-equation-at-a-point.htmlBuzz Spill Dailyen2026-08-27T10:49:18-04:00Can I solve this differential equation at a point?https://liberty.io/does-bounded-in-probability-imply-convergence-in-probability.htmlBuzz Spill Dailyen2026-08-27T10:48:24-04:00Does bounded in probability imply convergence in probability?https://liberty.io/proof-of-clarkson-039-s-inequality.htmlBuzz Spill Dailyen2026-08-27T10:43:45-04:00Proof of Clarkson's Inequalityhttps://liberty.io/what-are-some-of-the-best-textbooks-on-multi-objective-optimization.htmlBuzz Spill Dailyen2026-08-27T10:35:23-04:00What are some of the best textbooks on multi-objective optimization?https://liberty.io/why-is-homology-unable-to-distinguish-between-planar-and-non-planar-gr.htmlBuzz Spill Dailyen2026-08-27T10:26:06-04:00Why is homology unable to distinguish between planar and non-planar graphs?https://liberty.io/does-zeta-3-have-a-connection-with-pi.htmlBuzz Spill Dailyen2026-08-27T10:25:26-04:00Does $\zeta(3)$ have a connection with $\pi$?https://liberty.io/is-there-a-formula-for-the-roots-of-a-quintic-equation.htmlBuzz Spill Dailyen2026-08-27T10:23:36-04:00Is there a formula for the roots of a Quintic Equation?https://liberty.io/reference-for-harmonic-analysis.htmlBuzz Spill Dailyen2026-08-27T10:19:58-04:00Reference for Harmonic Analysis?https://liberty.io/are-all-eigenvectors-of-any-matrix-always-orthogonal.htmlBuzz Spill Dailyen2026-08-27T10:19:38-04:00Are all eigenvectors, of any matrix, always orthogonal?https://liberty.io/information-theory-data-processing-inequality.htmlBuzz Spill Dailyen2026-08-27T10:18:32-04:00Information Theory - Data Processing Inequalityhttps://liberty.io/game-theory-value-of-a-game.htmlBuzz Spill Dailyen2026-08-27T10:17:50-04:00Game theory:- value of a game?https://liberty.io/what-is-contour-integration.htmlBuzz Spill Dailyen2026-08-27T10:04:50-04:00What is contour integrationhttps://liberty.io/derivation-of-the-cubic-formula.htmlBuzz Spill Dailyen2026-08-27T10:02:52-04:00derivation of the cubic formulahttps://liberty.io/difference-between-scatter-plot-and-a-dotplot.htmlBuzz Spill Dailyen2026-08-27T10:02:17-04:00Difference between scatter-plot and a dotplothttps://liberty.io/the-function-f-z-x-z-zxz-defined-by-the-formula-f-m-n-5m-4n-4m-3n-is-b.htmlBuzz Spill Dailyen2026-08-27T09:40:13-04:00The function f: Z x Z -> ZxZ defined by the formula f(m,n) = (5m+4n, 4m+3n) is bijective. Then find its inverse.https://liberty.io/real-analysis-folland-problem-1-3-15-measures.htmlBuzz Spill Dailyen2026-08-27T09:31:08-04:00Real Analysis, Folland Problem 1.3.15 Measureshttps://liberty.io/what-is-the-significance-of-the-multiplicative-inverse.htmlBuzz Spill Dailyen2026-08-27T09:25:22-04:00What is the significance of the multiplicative inverse?https://liberty.io/phase-portrait-for-degenerate-node-duplicate.htmlBuzz Spill Dailyen2026-08-27T09:23:10-04:00Phase portrait for degenerate node [duplicate]https://liberty.io/find-the-coordinates-of-the-center-of-a-circle-with-circles-equations.htmlBuzz Spill Dailyen2026-08-27T09:19:13-04:00Find the coordinates of the center of a circle with circles equationshttps://liberty.io/calculus-3-sequences-and-series-closed.htmlBuzz Spill Dailyen2026-08-27T09:04:29-04:00calculus 3, sequences and series? [closed]https://liberty.io/what-exactly-is-a-probability-measure-in-simple-words.htmlBuzz Spill Dailyen2026-08-27T09:03:27-04:00What exactly is a probability measure in simple words?https://liberty.io/do-i-need-to-understand-multi-variable-calculus-to-study-linear-algebr.htmlBuzz Spill Dailyen2026-08-27T09:00:11-04:00Do I need to understand Multi-Variable Calculus to study Linear Algebra?https://liberty.io/is-there-always-a-superlinear-function-which-strongly-dominates-a-give.htmlBuzz Spill Dailyen2026-08-27T08:57:07-04:00Is there always a superlinear function which "strongly dominates" a given superlinear function?https://liberty.io/induction-problem-log-of-product-equals-sum-of-logs.htmlBuzz Spill Dailyen2026-08-27T08:52:08-04:00Induction problem: log of product equals sum of logshttps://liberty.io/laplace-039-s-equation-in-spherical-coordinates.htmlBuzz Spill Dailyen2026-08-27T08:48:38-04:00Laplace's Equation in Spherical Coordinateshttps://liberty.io/lp-relaxation-for-integer-linear-programming-ilp.htmlBuzz Spill Dailyen2026-08-27T08:39:23-04:00LP relaxation for integer linear programming (ILP)https://liberty.io/probability-that-two-random-numbers-are-coprime-is-frac-6-pi-2.htmlBuzz Spill Dailyen2026-08-27T08:30:13-04:00Probability that two random numbers are coprime is $\frac{6}{\pi^2}$