https://liberty.io/if-z-is-a-complex-number-whose-imaginary-part-is-non-zero-and-z-1-z-is.htmlBuzz Spill Dailyen2026-08-16T13:15:41-04:00If $z$ is a complex number whose imaginary part is non zero, and $z + 1/z $ is real, what is $z$?https://liberty.io/write-the-piecewise-function-in-terms-of-unit-step-functions.htmlBuzz Spill Dailyen2026-08-16T13:09:43-04:00Write the piecewise function in terms of unit step functionshttps://liberty.io/what-039-s-the-name-for-this-weird-shape-why-is-there-a-kite-inside-of.htmlBuzz Spill Dailyen2026-08-16T13:07:45-04:00What's the name for this weird shape? Why is there a kite inside of this triangle?https://liberty.io/example-of-a-function-that-is-not-continuous-at-0-0-but-continuous-whe.htmlBuzz Spill Dailyen2026-08-16T13:05:21-04:00Example of a function that is not continuous at $(0, 0)$ but continuous when restricted to any curve approaching the originhttps://liberty.io/the-mean-of-a-deterministic-sequence.htmlBuzz Spill Dailyen2026-08-16T12:59:33-04:00The mean of a deterministic sequencehttps://liberty.io/hexagon-maze-algorithm.htmlBuzz Spill Dailyen2026-08-16T12:52:16-04:00Hexagon "maze" algorithmhttps://liberty.io/the-rate-of-change-of-distance-between-two-airplanes-closed.htmlBuzz Spill Dailyen2026-08-16T12:50:41-04:00The rate of change of distance between two airplanes [closed]https://liberty.io/find-a-one-parameter-family-of-solutions.htmlBuzz Spill Dailyen2026-08-16T12:47:31-04:00Find a one parameter family of solutions?https://liberty.io/solve-x-x-5-5-for-x-duplicate.htmlBuzz Spill Dailyen2026-08-16T12:42:56-04:00Solve $x^{x^5} = 5$ for $x$ [duplicate]https://liberty.io/pronunciation-of-the-symbol-varnothing-of-the-empty-set.htmlBuzz Spill Dailyen2026-08-16T12:26:43-04:00Pronunciation of the symbol $\varnothing$ of the empty sethttps://liberty.io/herstein-or-herstein.htmlBuzz Spill Dailyen2026-08-16T12:23:50-04:00Herstein or Herstein?https://liberty.io/consistency-of-peano-axioms-hilbert-039-s-second-problem.htmlBuzz Spill Dailyen2026-08-16T12:14:46-04:00Consistency of Peano axioms (Hilbert's second problem)?https://liberty.io/fourier-transform-of-even-odd-function.htmlBuzz Spill Dailyen2026-08-16T12:04:56-04:00Fourier transform of even/odd functionhttps://liberty.io/solve-sqrt-x-2-4-x-2.htmlBuzz Spill Dailyen2026-08-16T12:00:20-04:00Solve: $\sqrt{x^2-4}=x-2$https://liberty.io/difference-between-maximum-and-minimum.htmlBuzz Spill Dailyen2026-08-16T11:55:49-04:00Difference between maximum and minimum?https://liberty.io/find-exact-value-of-tan-when-given-cos.htmlBuzz Spill Dailyen2026-08-16T11:53:18-04:00Find exact value of tan when given coshttps://liberty.io/simplify-this-problem-from-spivak-039-s-calculis.htmlBuzz Spill Dailyen2026-08-16T11:49:20-04:00Simplify this problem from Spivak's Calculis.https://liberty.io/what-039-s-the-geometrical-meaning-of-immersion.htmlBuzz Spill Dailyen2026-08-16T11:45:21-04:00What's the geometrical meaning of immersion?https://liberty.io/solve-for-x-in-e-2-ln-x-ln-x-2-x-3-1.htmlBuzz Spill Dailyen2026-08-16T11:43:21-04:00Solve for $x$ in: $e^{2\ln(x)-\ln(x^2+x-3)} = 1$https://liberty.io/establishing-a-covering-relation.htmlBuzz Spill Dailyen2026-08-16T11:41:29-04:00Establishing A Covering Relationhttps://liberty.io/a-curiosity-how-do-we-prove-mathbb-r-is-closed-under-addition-and-mult.htmlBuzz Spill Dailyen2026-08-16T11:38:11-04:00A curiosity: how do we prove $\mathbb{R}$ is closed under addition and multiplication?https://liberty.io/what-do-you-call-the-product-of-a-matrix-039-s-diagonal-elements.htmlBuzz Spill Dailyen2026-08-16T11:32:17-04:00What do you call the product of a matrix's diagonal elements?https://liberty.io/what-does-a-complex-root-signify.htmlBuzz Spill Dailyen2026-08-16T11:30:31-04:00What does a complex root signify?https://liberty.io/multiplicative-property-of-trace.htmlBuzz Spill Dailyen2026-08-16T11:24:20-04:00Multiplicative property of tracehttps://liberty.io/why-is-the-approximation-of-hessian-j-tj-reasonable.htmlBuzz Spill Dailyen2026-08-16T11:23:41-04:00Why is the approximation of Hessian$= J^TJ$ reasonable?https://liberty.io/convergence-in-distribution-of-differences-sums-of-random-variables.htmlBuzz Spill Dailyen2026-08-16T11:05:31-04:00Convergence in distribution of differences (sums) of random variableshttps://liberty.io/jordan-decomposition-of-idempotent-matrix.htmlBuzz Spill Dailyen2026-08-16T10:57:11-04:00Jordan decomposition of Idempotent matrix.https://liberty.io/is-every-vector-field-the-gradient-of-a-scalar-field.htmlBuzz Spill Dailyen2026-08-16T10:55:55-04:00Is every vector field the gradient of a scalar field?https://liberty.io/can-a-connected-eulerian-graph-have-an-even-number-of-vertices-and-an-.htmlBuzz Spill Dailyen2026-08-16T10:53:52-04:00Can a connected Eulerian graph have an even number of vertices and an odd number of edges?https://liberty.io/laplace-transform-of-derivatives.htmlBuzz Spill Dailyen2026-08-16T10:42:53-04:00Laplace transform of derivativeshttps://liberty.io/why-isn-039-t-1900-a-leap-year-closed.htmlBuzz Spill Dailyen2026-08-16T10:41:48-04:00Why isn't 1900 a leap year? [closed]https://liberty.io/how-do-i-find-the-taylor-series-of-f-x-5cos-x-a-11pi.htmlBuzz Spill Dailyen2026-08-16T10:39:26-04:00How do I find the Taylor series of f(x) = 5cos(x), a = 11pi????https://liberty.io/are-there-any-examples-of-non-computable-real-numbers.htmlBuzz Spill Dailyen2026-08-16T10:19:50-04:00Are there any examples of non-computable real numbers?https://liberty.io/prove-that-the-values-of-x-for-which-x-frac-x-2-1-198-lie-between-frac.htmlBuzz Spill Dailyen2026-08-16T10:08:11-04:00Prove that the values of $x$ for which $x = \frac{x^2+1}{198}$ lie between $\frac{1}{198}$ and $199.99 \overline{49}$.https://liberty.io/showing-a-function-does-not-have-a-local-max-or-min.htmlBuzz Spill Dailyen2026-08-16T09:58:10-04:00Showing a function does not have a local max or minhttps://liberty.io/show-that-the-square-of-any-prime-number-is-the-factof-of-some-integer.htmlBuzz Spill Dailyen2026-08-16T09:54:33-04:00Show that the square of any prime number is the Factof of some integerhttps://liberty.io/complementary-subspaces.htmlBuzz Spill Dailyen2026-08-16T09:26:41-04:00Complementary Subspaces .https://liberty.io/how-does-this-definition-of-the-exponential-function-have-e-0-1.htmlBuzz Spill Dailyen2026-08-16T09:24:41-04:00How does this definition of the exponential function have E(0)=1?https://liberty.io/vector-analysis-calculate-the-flux-of-the-vector-field-s.htmlBuzz Spill Dailyen2026-08-16T09:15:41-04:00Vector analysis: Calculate the flux of the vector field Shttps://liberty.io/how-to-represent-a-decimal-number-in-ternary-or-base-3-number-system.htmlBuzz Spill Dailyen2026-08-16T09:13:47-04:00How to represent a decimal number in ternary or base $3$ number system?https://liberty.io/arithmetic-mean-why-does-it-work.htmlBuzz Spill Dailyen2026-08-16T09:08:41-04:00Arithmetic mean. Why does it work?https://liberty.io/user-ashvin-swaminathan-mathematics-stack-exchange.htmlBuzz Spill Dailyen2026-08-16T09:06:51-04:00User Ashvin Swaminathan - Mathematics Stack Exchangehttps://liberty.io/second-partial-derivative-test-failing-when-determinant-is-0.htmlBuzz Spill Dailyen2026-08-16T09:05:20-04:00Second partial derivative test failing when Determinant is 0https://liberty.io/describing-asymptotic-behaviour-of-a-function.htmlBuzz Spill Dailyen2026-08-16T09:03:31-04:00Describing asymptotic behaviour of a functionhttps://liberty.io/which-geometric-figure-polyhedron-has-15-quadrilateral-faces.htmlBuzz Spill Dailyen2026-08-16T09:02:27-04:00Which geometric figure (polyhedron) has 15 quadrilateral faces?https://liberty.io/evaluating-2x-3-9x-2-10x-13-for-x-3-sqrt-5-is-there-an-efficient-way-t.htmlBuzz Spill Dailyen2026-08-16T08:56:38-04:00Evaluating $2x^3-9x^2-10x+13$ for $x=3+\sqrt{5}$. Is there an efficient way to tell that this reduces to $1$?https://liberty.io/example-of-distinctions-between-multiple-integral-and-iterated-integra.htmlBuzz Spill Dailyen2026-08-16T08:45:30-04:00Example of distinctions between multiple integral and iterated integrals.https://liberty.io/cardioid-in-coffee-mug.htmlBuzz Spill Dailyen2026-08-16T08:44:14-04:00Cardioid in coffee mug?https://liberty.io/the-expected-value-of-the-square-of-sample-variance.htmlBuzz Spill Dailyen2026-08-16T08:43:46-04:00The expected-value of the square of Sample Variance.https://liberty.io/show-that-the-volume-of-a-sphere-of-radius-r-is-v-frac-4-3-pi-r-3.htmlBuzz Spill Dailyen2026-08-16T08:37:32-04:00Show that the volume of a sphere of radius $r$ is $V = \frac{4}{3} \pi r^3$https://liberty.io/fourier-transform-of-e-iwt.htmlBuzz Spill Dailyen2026-08-16T08:37:09-04:00Fourier transform of $e^{-iwt}$https://liberty.io/does-convergence-in-distribution-implies-convergence-of-characteristic.htmlBuzz Spill Dailyen2026-08-16T08:34:13-04:00Does convergence in distribution implies convergence of characteristic functions?https://liberty.io/how-do-i-solve-this-quadratic-equation-with-a-fraction.htmlBuzz Spill Dailyen2026-08-16T08:30:21-04:00how do I solve this quadratic equation with a fraction?https://liberty.io/when-the-population-variance-is-unknown-we-should-use-t-distribution.htmlBuzz Spill Dailyen2026-08-16T08:29:18-04:00When the population variance is unknown, we should use t-distribution.https://liberty.io/sigma-algebra-generated-by-two-sigma-algebras-is-generated-by-the-inte.htmlBuzz Spill Dailyen2026-08-16T08:27:02-04:00sigma-algebra generated by two-sigma algebras is generated by the intersection of sets from these two sigma-algebrahttps://liberty.io/how-to-find-dy-dx-fx-fy.htmlBuzz Spill Dailyen2026-08-16T08:06:18-04:00How to find dy/dx = - fx/fy?https://liberty.io/difference-between-power-law-distribution-and-exponential-decay.htmlBuzz Spill Dailyen2026-08-16T08:03:11-04:00Difference between power law distribution and exponential decayhttps://liberty.io/probability-a-flaw-in-logic-the-emperor-039-s-proposition-with-marbles.htmlBuzz Spill Dailyen2026-08-16T08:02:11-04:00Probability: A flaw in logic? The emperor's proposition with marbles and two urnshttps://liberty.io/prove-that-two-equations-are-the-same-if-they-have-the-same-solution-s.htmlBuzz Spill Dailyen2026-08-16T08:01:43-04:00Prove that two equations are the same if they have the same solution setshttps://liberty.io/directional-derivative-finding-a-line-equation.htmlBuzz Spill Dailyen2026-08-16T07:55:57-04:00Directional derivative , finding a line equationhttps://liberty.io/using-the-pumping-lemma-to-show-that-a-language-is-not-regular-compute.htmlBuzz Spill Dailyen2026-08-16T07:50:05-04:00Using the pumping lemma to show that a language is not regular (Computer Science)https://liberty.io/solving-for-x-with-exponents-algebra.htmlBuzz Spill Dailyen2026-08-16T07:47:51-04:00Solving for x with exponents (algebra)https://liberty.io/calculate-the-minimum-number-of-moves-required-to-solve-the-tower-of-h.htmlBuzz Spill Dailyen2026-08-16T07:35:02-04:00Calculate the minimum number of moves required to solve "The Tower of Hanoi" with $4$ pegs and $4$ discs.https://liberty.io/what-039-s-the-difference-between-a-dependent-function-type-pi-types-a.htmlBuzz Spill Dailyen2026-08-16T07:33:18-04:00What's the difference between a dependent function type$ ( \Pi - types) $ and a family of types?https://liberty.io/distance-between-the-two-points-p-and-q.htmlBuzz Spill Dailyen2026-08-16T07:33:00-04:00Distance between the two points $P$ and $Q$https://liberty.io/how-to-determine-concavity-without-inflection-point.htmlBuzz Spill Dailyen2026-08-16T07:29:28-04:00How to determine concavity without inflection point?https://liberty.io/discrete-math-inclusive-or-vs-exclusive-or.htmlBuzz Spill Dailyen2026-08-16T07:28:42-04:00Discrete Math Inclusive or VS Exclusive orhttps://liberty.io/how-to-solve-equations-with-casio-fx-85wa-calculator.htmlBuzz Spill Dailyen2026-08-16T07:24:24-04:00How to solve equations with Casio FX-85WA calculatorhttps://liberty.io/is-blitzer-precalculus-my-best-option-considering-my-circumstances.htmlBuzz Spill Dailyen2026-08-16T07:18:03-04:00Is Blitzer Precalculus my best option considering my circumstances?https://liberty.io/weighted-probability-problem.htmlBuzz Spill Dailyen2026-08-16T07:18:00-04:00Weighted Probability Problemhttps://liberty.io/area-of-a-regular-hexagon-via-area-of-triangles.htmlBuzz Spill Dailyen2026-08-16T06:55:41-04:00Area of a regular hexagon via area of triangleshttps://liberty.io/determinant-of-a-very-large-matrix-in-matlab.htmlBuzz Spill Dailyen2026-08-16T06:47:40-04:00determinant of a very large matrix in MATLABhttps://liberty.io/why-does-fixed-point-iteration-work.htmlBuzz Spill Dailyen2026-08-16T06:39:02-04:00Why does Fixed Point Iteration work?https://liberty.io/derivative-of-sin-2x-cos-3x.htmlBuzz Spill Dailyen2026-08-16T06:33:23-04:00Derivative of $\sin (2x)\cos(3x)$https://liberty.io/identifying-the-formula-for-a-quartic-graphic.htmlBuzz Spill Dailyen2026-08-16T06:30:56-04:00Identifying the formula for a quartic graphichttps://liberty.io/what-is-the-kernel-of-a-homomorphism.htmlBuzz Spill Dailyen2026-08-16T06:29:31-04:00What is the kernel of a homomorphism?https://liberty.io/intuition-for-class-numbers.htmlBuzz Spill Dailyen2026-08-16T06:24:08-04:00Intuition for Class Numbershttps://liberty.io/implicit-derivative-with-three-variable.htmlBuzz Spill Dailyen2026-08-16T06:19:06-04:00Implicit Derivative with Three Variablehttps://liberty.io/why-do-we-say-the-harmonic-series-is-divergent-duplicate.htmlBuzz Spill Dailyen2026-08-16T06:18:30-04:00Why do we say the harmonic series is divergent? [duplicate]https://liberty.io/how-to-understand-compactness-duplicate.htmlBuzz Spill Dailyen2026-08-16T06:11:14-04:00How to understand compactness? [duplicate]https://liberty.io/why-is-it-possible-to-factor-a-limit.htmlBuzz Spill Dailyen2026-08-16T06:08:14-04:00why is it possible to factor a limit?https://liberty.io/finding-the-splitting-field-of-a-polynomial.htmlBuzz Spill Dailyen2026-08-16T06:06:14-04:00Finding the splitting field of a polynomial.https://liberty.io/slope-of-secant-and-tangent-lines-supported-by-mvt.htmlBuzz Spill Dailyen2026-08-16T06:00:00-04:00Slope of secant and tangent lines (supported by MVT)https://liberty.io/where-was-my-mistake-integration-by-trig-substitution-problem.htmlBuzz Spill Dailyen2026-08-16T05:59:58-04:00Where was my mistake (integration by trig-substitution problem)?https://liberty.io/how-to-calculate-modulo-negative-number-duplicate.htmlBuzz Spill Dailyen2026-08-16T05:59:21-04:00How to calculate modulo negative number? [duplicate]https://liberty.io/is-there-any-equation-for-triangle.htmlBuzz Spill Dailyen2026-08-16T05:57:33-04:00Is there any equation for triangle?https://liberty.io/if-capital-letters-are-supposed-to-be-sets-why-is-n-used-as-a-number.htmlBuzz Spill Dailyen2026-08-16T05:45:39-04:00If capital letters are supposed to be sets, why is $N$ used as a number?https://liberty.io/a-line-connecting-an-interior-and-an-exterior-point-of-a-circle-should.htmlBuzz Spill Dailyen2026-08-16T05:24:37-04:00A line connecting an interior and an exterior point of a circle should intersect the circle at some pointhttps://liberty.io/information-gain-calculation-for-decision-tree-when-choosing-root-node.htmlBuzz Spill Dailyen2026-08-16T05:09:17-04:00Information gain calculation for decision tree when choosing root nodehttps://liberty.io/can-you-integrate-without-a-dx-duplicate.htmlBuzz Spill Dailyen2026-08-16T05:07:23-04:00Can you integrate without a $dx$ [duplicate]https://liberty.io/fisher-yates-algorithm-proof.htmlBuzz Spill Dailyen2026-08-16T05:05:12-04:00Fisher-Yates algorithm proofhttps://liberty.io/what-does-p-a-u-b-mean-in-terms-of-real-values.htmlBuzz Spill Dailyen2026-08-16T05:02:40-04:00What does P(A U B) mean, in terms of real values?https://liberty.io/prove-det-i-m-ab-det-i-n-ba-duplicate.htmlBuzz Spill Dailyen2026-08-16T04:42:35-04:00Prove $\det(I_m + AB) = \det(I_n + BA)$. [duplicate]https://liberty.io/in-matrix-notation-what-does-it-mean-x-039-x.htmlBuzz Spill Dailyen2026-08-16T04:37:23-04:00In Matrix notation what does it mean X 'Xhttps://liberty.io/help-me-to-find-a-volume-of-the-ring-shaped-solid.htmlBuzz Spill Dailyen2026-08-16T04:24:26-04:00help me to find a volume of the ring shaped solidhttps://liberty.io/inverse-of-a-1-b-1.htmlBuzz Spill Dailyen2026-08-16T04:20:15-04:00Inverse of $A^{-1}+B^{-1}$https://liberty.io/find-limit-of-a-n-ln-1-a-n-1.htmlBuzz Spill Dailyen2026-08-16T04:12:04-04:00Find limit of $a_n = \ln (1 + a_{n-1})$https://liberty.io/jacobson-039-s-density-theorem-for-semisimple-algebras.htmlBuzz Spill Dailyen2026-08-16T04:06:22-04:00Jacobson's Density Theorem for Semisimple Algebrashttps://liberty.io/mod-remainder-operation-and-relation-name-and-meaning.htmlBuzz Spill Dailyen2026-08-16T04:04:12-04:00mod [= remainder] operation (and relation), name and meaninghttps://liberty.io/duffing-oscillator.htmlBuzz Spill Dailyen2026-08-16T03:58:59-04:00Duffing oscillator