https://pop.com.sg/what-is-the-mutual-information-i-x-x.htmlFame Craze Newsen2026-08-19T02:44:11-04:00What is the mutual information $I(X;X)$?https://pop.com.sg/l0-norm-l1-norm-and-l2-norm.htmlFame Craze Newsen2026-08-19T02:43:20-04:00L0 norm, L1 norm and L2 normhttps://pop.com.sg/what-does-a-compact-set-look-like.htmlFame Craze Newsen2026-08-19T02:40:13-04:00What does a compact set look like?https://pop.com.sg/help-me-to-understand-the-potato-paradox.htmlFame Craze Newsen2026-08-19T02:37:16-04:00Help me to understand the potato paradoxhttps://pop.com.sg/proving-de-morgan-039-s-generalized-laws.htmlFame Craze Newsen2026-08-19T02:25:16-04:00Proving De Morgan's Generalized Lawshttps://pop.com.sg/what-is-meant-by-passing-to-a-subsequence.htmlFame Craze Newsen2026-08-19T02:22:33-04:00What is meant by "passing to a subsequence"?https://pop.com.sg/explanation-of-the-formula-for-combinations-without-repetition-probabi.htmlFame Craze Newsen2026-08-19T02:21:36-04:00Explanation of the formula for combinations without repetition, probabilityhttps://pop.com.sg/why-do-you-need-three-perpendicular-bisectors-to-circumscribe-a-triang.htmlFame Craze Newsen2026-08-19T02:11:21-04:00Why do you need three perpendicular bisectors to circumscribe a triangle?https://pop.com.sg/homeomorphic-graphs.htmlFame Craze Newsen2026-08-19T02:09:55-04:00homeomorphic graphshttps://pop.com.sg/muddy-children-puzzle-when-more-than-2-kids-are-muddy.htmlFame Craze Newsen2026-08-19T01:53:43-04:00Muddy Children Puzzle (when more than 2 kids are muddy)https://pop.com.sg/how-to-find-an-angle-in-degrees-in-a-right-triangle-given-its-sides.htmlFame Craze Newsen2026-08-19T01:50:17-04:00How to find an angle (in degrees) in a right triangle, given its sides?https://pop.com.sg/finding-minimum-value-of-sqrt-x-2-y-2-duplicate.htmlFame Craze Newsen2026-08-19T01:49:26-04:00Finding minimum value of $\sqrt{x^2+y^2}$ [duplicate]https://pop.com.sg/questions-tagged-definite-integrals.htmlFame Craze Newsen2026-08-19T01:36:31-04:00Questions tagged [definite-integrals] https://pop.com.sg/is-there-a-name-for-a-3d-shape-that-looks-like-a-circle-when-viewed-fr.htmlFame Craze Newsen2026-08-19T01:28:36-04:00Is there a name for a 3D shape that looks like a circle when viewed from one axis, a square from another, and a triangle from the third?https://pop.com.sg/is-there-a-three-dimensional-version-of-curl-in-which-the-result-is-a-.htmlFame Craze Newsen2026-08-19T01:23:40-04:00Is there a three-dimensional version of curl in which the result is a vector?https://pop.com.sg/domain-of-exponential-function.htmlFame Craze Newsen2026-08-19T01:16:39-04:00Domain of exponential functionhttps://pop.com.sg/bounded-vs-unbounded-linear-programs.htmlFame Craze Newsen2026-08-19T01:14:51-04:00bounded vs. unbounded linear programshttps://pop.com.sg/real-analysis-continuity-of-a-composition-function.htmlFame Craze Newsen2026-08-19T01:12:20-04:00Real Analysis: Continuity of a Composition Functionhttps://pop.com.sg/how-to-show-cubic-function-is-one-to-one-using-assumption.htmlFame Craze Newsen2026-08-19T01:07:46-04:00how to show cubic function is one to one using assumptionhttps://pop.com.sg/integrate-over-an-area-of-a-parabola.htmlFame Craze Newsen2026-08-19T01:06:24-04:00Integrate over an area of a parabolahttps://pop.com.sg/centroid-root-locus.htmlFame Craze Newsen2026-08-19T01:02:44-04:00Centroid Root Locushttps://pop.com.sg/why-is-establishing-absolute-consistency-of-zfc-impossible.htmlFame Craze Newsen2026-08-19T00:57:45-04:00Why is establishing absolute consistency of ZFC impossible?https://pop.com.sg/what-is-the-conjugate-of-i-iota.htmlFame Craze Newsen2026-08-19T00:35:46-04:00What is the conjugate of $i$ (iota)?https://pop.com.sg/prove-the-derivative-of-sin-1-x-exists.htmlFame Craze Newsen2026-08-19T00:26:12-04:00Prove the derivative of $\sin(1/x)$ existshttps://pop.com.sg/how-many-possible-3-character-combinations-using-letters-closed.htmlFame Craze Newsen2026-08-19T00:08:29-04:00How many possible 3 character combinations using letters? [closed]https://pop.com.sg/convert-quaternion-to-vector-closed.htmlFame Craze Newsen2026-08-19T00:03:11-04:00Convert quaternion to vector? [closed]https://pop.com.sg/18-people-divided-into-3-groups-probability.htmlFame Craze Newsen2026-08-19T00:00:36-04:0018 people divided into 3 groups probabilityhttps://pop.com.sg/into-function-vs-injective-function.htmlFame Craze Newsen2026-08-18T23:53:25-04:00into function vs injective functionhttps://pop.com.sg/transformations-from-n-sphere-coordinates-to-cartesian-coordinates.htmlFame Craze Newsen2026-08-18T23:53:10-04:00Transformations from n-sphere coordinates to cartesian coordinates.https://pop.com.sg/solid-angle-integration.htmlFame Craze Newsen2026-08-18T23:40:21-04:00Solid angle: integrationhttps://pop.com.sg/fundamental-theorem-of-calculus-of-a-definite-integral.htmlFame Craze Newsen2026-08-18T23:39:27-04:00Fundamental Theorem of Calculus of a definite integralhttps://pop.com.sg/prime-numbers-6k-1-mod-rule-new-discovery.htmlFame Craze Newsen2026-08-18T23:38:22-04:00Prime Numbers: 6k-1 mod rule (New Discovery?)https://pop.com.sg/understanding-the-properties-and-use-of-the-laplacian-matrix-and-its-n.htmlFame Craze Newsen2026-08-18T23:27:55-04:00Understanding the properties and use of the Laplacian matrix (and its norm)https://pop.com.sg/is-0-a-natural-number.htmlFame Craze Newsen2026-08-18T23:21:00-04:00Is $0$ a natural number?https://pop.com.sg/what-is-wrong-with-my-solution-int-cos-2-x-tan-3x-dx.htmlFame Craze Newsen2026-08-18T23:17:46-04:00What is wrong with my solution? $\int \cos^2 x \tan^3x dx$https://pop.com.sg/what-allows-us-divide-multiply-dx-in-calculus.htmlFame Craze Newsen2026-08-18T23:16:08-04:00What allows us divide/multiply dx in calculus?https://pop.com.sg/what-is-general-term-of-the-sequence-1-2-4-4-8-8-8-8-16-16-16-16-16-16.htmlFame Craze Newsen2026-08-18T23:16:02-04:00What is general term of the sequence : $1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32 ...$?https://pop.com.sg/how-to-find-a-minimal-polynomial.htmlFame Craze Newsen2026-08-18T23:11:00-04:00How to find a minimal polynomialhttps://pop.com.sg/laplace-transform-of-sin-at-by-definition.htmlFame Craze Newsen2026-08-18T23:08:22-04:00Laplace transform of $\sin(at)$ by definitionhttps://pop.com.sg/what-is-temperature-distribution-equation.htmlFame Craze Newsen2026-08-18T23:04:52-04:00What is temperature distribution equation?https://pop.com.sg/minimal-realization-of-a-state-space-model.htmlFame Craze Newsen2026-08-18T23:03:41-04:00Minimal realization of a state space model?https://pop.com.sg/what-does-it-mean-to-solve-or-find-solutions-in-mathematics.htmlFame Craze Newsen2026-08-18T22:49:57-04:00What does it mean to solve or find solutions in mathematics?https://pop.com.sg/find-a-vector-mathbf-x-whose-image-under-t-is-b.htmlFame Craze Newsen2026-08-18T22:24:16-04:00Find a vector $\mathbf x$ whose image under $T$ is $b$.https://pop.com.sg/calculating-multivariable-limit.htmlFame Craze Newsen2026-08-18T22:20:48-04:00Calculating multivariable limithttps://pop.com.sg/how-do-i-determine-if-a-matrix-is-in-a-span-of-two-other-matrices.htmlFame Craze Newsen2026-08-18T22:13:32-04:00How do I determine if a matrix is in a span of two other matrices?https://pop.com.sg/degeneracy-of-outerplanar-graphs.htmlFame Craze Newsen2026-08-18T22:04:07-04:00Degeneracy of outerplanar graphshttps://pop.com.sg/period-vs-time-period-of-sine-wave.htmlFame Craze Newsen2026-08-18T21:47:43-04:00period vs time period of sine wavehttps://pop.com.sg/determine-if-a-statement-is-true-or-false.htmlFame Craze Newsen2026-08-18T21:33:43-04:00Determine if a statement is true or falsehttps://pop.com.sg/manual-calculation-doesn-039-t-match-wolfram-alpha-why.htmlFame Craze Newsen2026-08-18T21:32:34-04:00Manual calculation doesn't match Wolfram Alpha. Why?https://pop.com.sg/simplifying-math-equation-with-factorials.htmlFame Craze Newsen2026-08-18T21:28:43-04:00simplifying math equation with factorialshttps://pop.com.sg/find-the-perimeter-of-the-trapezoid-from-the-3-side-lengths.htmlFame Craze Newsen2026-08-18T21:27:38-04:00Find the perimeter of the trapezoid from the 3 side lengths.https://pop.com.sg/there-is-any-relation-between-pi-sqrt-2-or-a-generic-polygon.htmlFame Craze Newsen2026-08-18T21:24:00-04:00there is any relation between $\pi$, $\sqrt{2}$ or a generic polygon?https://pop.com.sg/probability-of-3-people-in-a-room-of-30-having-the-same-birthday.htmlFame Craze Newsen2026-08-18T21:21:30-04:00Probability of 3 people in a room of 30 having the same birthdayhttps://pop.com.sg/solve-the-function-for-x-in-terms-of-y.htmlFame Craze Newsen2026-08-18T21:19:39-04:00Solve the function for $x$ in terms of $y$https://pop.com.sg/solve-equation-with-absolute-value-of-complex-numbers.htmlFame Craze Newsen2026-08-18T21:18:35-04:00Solve equation with absolute value of complex numbershttps://pop.com.sg/how-to-perform-abstract-integration.htmlFame Craze Newsen2026-08-18T21:12:39-04:00How to perform abstract integrationhttps://pop.com.sg/zebra-groups-and-counting-stripes.htmlFame Craze Newsen2026-08-18T20:53:10-04:00Zebra groups and counting stripeshttps://pop.com.sg/what-is-the-difference-between-shifting-functions-and-shifting-parabol.htmlFame Craze Newsen2026-08-18T20:51:10-04:00What is the difference between shifting functions and shifting parabolas?https://pop.com.sg/limit-of-absolute-values.htmlFame Craze Newsen2026-08-18T20:50:10-04:00limit of absolute valueshttps://pop.com.sg/why-is-this-called-the-cocycle-condition.htmlFame Craze Newsen2026-08-18T20:38:56-04:00Why is this called the cocycle condition?https://pop.com.sg/integration-involving-fractional-part-function.htmlFame Craze Newsen2026-08-18T20:38:36-04:00Integration involving fractional part functionhttps://pop.com.sg/is-a-linear-transformation-onto-or-one-to-one.htmlFame Craze Newsen2026-08-18T20:34:37-04:00Is a linear transformation onto or one-to-one?https://pop.com.sg/what-does-it-mean-for-media-to-play-at-1-5x-or-nx-speed.htmlFame Craze Newsen2026-08-18T20:31:20-04:00What does it mean for media to play at "1.5x" or (Nx) speed?https://pop.com.sg/find-all-eigenvalues-of-a-matrix-that-holds-a-a-5.htmlFame Craze Newsen2026-08-18T20:20:48-04:00Find all eigenvalues of a matrix that holds $A = A^{5}$https://pop.com.sg/adjoint-of-a-differential-operator.htmlFame Craze Newsen2026-08-18T20:20:24-04:00Adjoint of a differential operatorhttps://pop.com.sg/why-is-congruence-sign-a-equiv-b-pmod-c-closed.htmlFame Craze Newsen2026-08-18T20:16:42-04:00Why is congruence sign $A\equiv B\pmod{C}$? [closed]https://pop.com.sg/vi-arnold-ode-need-help-coming-to-grips-with-early-notation-in-the-boo.htmlFame Craze Newsen2026-08-18T20:06:10-04:00VI Arnold ODE: Need help coming to grips with early notation in the book (phase velocity)https://pop.com.sg/fair-coin-and-weighted-coin.htmlFame Craze Newsen2026-08-18T20:05:46-04:00Fair coin and weighted coinhttps://pop.com.sg/how-can-2-100-2-98-2-99-2-97-be-written-in-terms-of-its-prime-factors.htmlFame Craze Newsen2026-08-18T19:56:31-04:00How can $(2^{100}-2^{98})(2^{99}-2^{97})$ be written in terms of its prime factors?https://pop.com.sg/domain-and-range-of-piecewise-function-help.htmlFame Craze Newsen2026-08-18T19:53:18-04:00Domain and Range of Piecewise Function Helphttps://pop.com.sg/how-to-find-sin-and-cos-of-0-pi-2-pi-without-calculator-closed.htmlFame Craze Newsen2026-08-18T19:36:22-04:00How to find sin and cos of 0, pi/2, pi without calculator [closed]https://pop.com.sg/degenerate-solution-in-linear-programming.htmlFame Craze Newsen2026-08-18T19:21:47-04:00Degenerate solution in linear programminghttps://pop.com.sg/proof-of-bolzano-039-s-theorem.htmlFame Craze Newsen2026-08-18T19:19:37-04:00Proof of Bolzano's Theoremhttps://pop.com.sg/explanation-of-the-derivation-of-the-formula-for-the-sum-of-an-arithme.htmlFame Craze Newsen2026-08-18T19:14:08-04:00Explanation of the derivation of the formula for the sum of an arithmetic sequence of the first n termshttps://pop.com.sg/polynomial-function-given-roots-and-a-point.htmlFame Craze Newsen2026-08-18T19:11:17-04:00Polynomial Function given roots and a pointhttps://pop.com.sg/how-to-find-the-transition-matrix-for-ordered-basis-of-2x2-diagonal-ma.htmlFame Craze Newsen2026-08-18T19:08:21-04:00How to find the transition matrix for ordered basis of 2x2 diagonal matriceshttps://pop.com.sg/what-does-inversion-mean.htmlFame Craze Newsen2026-08-18T19:07:40-04:00What does inversion mean?https://pop.com.sg/why-does-a-flat-finite-type-morphism-of-irreducible-noetherian-schemes.htmlFame Craze Newsen2026-08-18T19:04:30-04:00Why does a flat finite type morphism of irreducible noetherian schemes map generic pt to generic pthttps://pop.com.sg/let-f-k-be-two-fields-f-subset-k-and-suppose-f-x-g-x-in-f-x-are-relati.htmlFame Craze Newsen2026-08-18T19:04:24-04:00Let $F,K$ be two fields $F \subset K$ and suppose $f(x),g(x) \in F[x]$ are relatively prime in $F[x].$ Prove they are relatively prime in $K[x].$https://pop.com.sg/four-men-hats-and-probability.htmlFame Craze Newsen2026-08-18T19:04:10-04:00Four men, hats and probabilityhttps://pop.com.sg/finding-polynomal-function-with-given-zeros-and-one-zero-is-a-square-r.htmlFame Craze Newsen2026-08-18T19:03:24-04:00Finding polynomal function with given zeros and one zero is a square roothttps://pop.com.sg/what-is-the-domain-of-z-arcsin-dfrac-x-y.htmlFame Craze Newsen2026-08-18T19:02:19-04:00What is the domain of $z=\arcsin\dfrac{x}{y}$?https://pop.com.sg/difference-between-variance-and-covariance.htmlFame Craze Newsen2026-08-18T18:54:23-04:00difference between variance and covariancehttps://pop.com.sg/area-of-intersection-between-two-circles-duplicate.htmlFame Craze Newsen2026-08-18T18:51:26-04:00Area of intersection between two circles [duplicate]https://pop.com.sg/how-does-one-prove-rodrigues-039-formula-for-legendre-polynomials.htmlFame Craze Newsen2026-08-18T18:44:45-04:00How does one prove Rodrigues' formula for Legendre Polynomials?https://pop.com.sg/what-algebraic-topology-book-to-read-after-hatcher-039-s.htmlFame Craze Newsen2026-08-18T18:38:16-04:00What algebraic topology book to read after Hatcher's?https://pop.com.sg/finding-magnitude-of-a-function.htmlFame Craze Newsen2026-08-18T18:29:02-04:00Finding magnitude of a functionhttps://pop.com.sg/swing-twist-decomposition-for-quaternion-rotations-verification.htmlFame Craze Newsen2026-08-18T18:15:28-04:00Swing-Twist decomposition for quaternion rotations (verification)https://pop.com.sg/what-is-the-maximum-norm-induced-by-the-maximum-norm-for-mathbb-r-n.htmlFame Craze Newsen2026-08-18T18:10:31-04:00What is the maximum norm induced by the maximum norm for $\mathbb{R}^n$?https://pop.com.sg/how-is-the-joint-proportionality-joint-variation-equation-i-e-y-kxz-lo.htmlFame Craze Newsen2026-08-18T18:10:19-04:00How is the joint proportionality (joint variation) equation (i.e. $y = kxz$) logically correct?https://pop.com.sg/does-the-series-sum-frac-1-n-ln-n-3-2-converge-or-diverge.htmlFame Craze Newsen2026-08-18T18:03:03-04:00Does the series $\sum \frac{1}{n\ (\ln(n))^{3/2}}$ converge or diverge?https://pop.com.sg/derivative-of-arcsin-x-in-1.htmlFame Craze Newsen2026-08-18T18:01:01-04:00Derivative of $\arcsin(x)$ in $-1$https://pop.com.sg/rolling-a-fair-die.htmlFame Craze Newsen2026-08-18T18:00:25-04:00Rolling a fair diehttps://pop.com.sg/find-the-area-common-to-the-inside-of-the-cardioid-r-1-sin-theta-and-t.htmlFame Craze Newsen2026-08-18T18:00:14-04:00Find the area common to the inside of the cardioid $r = 1+\sin \theta$ and the outside of the cardioid $r = 1 + \cos \theta$.https://pop.com.sg/prove-sinh-x-x-for-all-x-0.htmlFame Craze Newsen2026-08-18T17:57:25-04:00Prove $\sinh x > x$ for all $x >0$https://pop.com.sg/find-arcsin-frac-4-5-arccos-frac-1-sqrt-50.htmlFame Craze Newsen2026-08-18T17:55:25-04:00Find $\arcsin(\frac{4}{5})+\arccos(\frac{1}{\sqrt{50}})$https://pop.com.sg/property-of-a-kite-inscribed-in-a-square.htmlFame Craze Newsen2026-08-18T17:41:45-04:00Property of a kite inscribed in a squarehttps://pop.com.sg/what-distinguishes-039-family-039-vs-039-set-039-of-functions.htmlFame Craze Newsen2026-08-18T17:41:18-04:00What distinguishes 'family' vs. 'set' of functions?https://pop.com.sg/a-question-about-irreducible-representations-of-so-3-group.htmlFame Craze Newsen2026-08-18T17:34:26-04:00A question about irreducible representations of SO(3) grouphttps://pop.com.sg/evaluating-int-2x-2-1-e-x-2-dx.htmlFame Craze Newsen2026-08-18T17:18:29-04:00Evaluating $\int(2x^2+1)e^{x^2}dx$