# OCME — Open Chinese Mathematical Encyclopedia > Bilingual public mathematics: statements, assumptions, dependencies, candidate questions and explicit evidence boundaries. HTML pages are readable without JavaScript. Interactive behavior is optional. All readers receive the same public projection. 302 knowledge objects; 36000 candidate questions. Mechanical checks are not human review or universal proof. No authorization for model training is inferred from this guide; existing licenses and robots.txt remain separate. ## Browse - [Home](https://ocme.evemisslab.com/index.md) - [Chinese atlas](https://ocme.evemisslab.com/zh-Hant/atlas/index.md) - [English knowledge](https://ocme.evemisslab.com/en/knowledge/index.md) - [Chinese question batches](https://ocme.evemisslab.com/zh-Hant/practice/index.md) - [English question batches](https://ocme.evemisslab.com/en/practice/index.md) - [Proof boundaries](https://ocme.evemisslab.com/en/formal/index.md) ## Knowledge and question lookup - [Chinese lookup](https://ocme.evemisslab.com/zh-Hant/explore/index.md) - [English lookup](https://ocme.evemisslab.com/en/explore/index.md) - [Exact question-number example](https://ocme.evemisslab.com/en/explore/index.json?q=36000) - [Public lookup metadata](https://ocme.evemisslab.com/data/explore/meta.json) GET filters: q (number, full question ID or title), mko, family, batch, state and page. HTML, Markdown and JSON share filters. Discovery returns existing candidates; source questions remain candidate and English remains ai_candidate. ## Knowledge objects - [Points, lines, and planes](https://ocme.evemisslab.com/en/mko/mko-point-line-plane/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-point-line-plane/index.md - [Angle](https://ocme.evemisslab.com/en/mko/mko-angle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-angle/index.md - [Triangle](https://ocme.evemisslab.com/en/mko/mko-triangle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-triangle/index.md - [Right triangle](https://ocme.evemisslab.com/en/mko/mko-right-triangle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-right-triangle/index.md - [Euclidean length](https://ocme.evemisslab.com/en/mko/mko-euclidean-length/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euclidean-length/index.md - [Pythagorean theorem](https://ocme.evemisslab.com/en/mko/mko-euclid-pythagorean-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euclid-pythagorean-theorem/index.md - [Natural number](https://ocme.evemisslab.com/en/mko/mko-natural-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-natural-number/index.md - [Integer](https://ocme.evemisslab.com/en/mko/mko-integer/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-integer/index.md - [Rational number](https://ocme.evemisslab.com/en/mko/mko-rational-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-rational-number/index.md - [Real number](https://ocme.evemisslab.com/en/mko/mko-real-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-number/index.md - [Arithmetic operations](https://ocme.evemisslab.com/en/mko/mko-arithmetic-operations/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-arithmetic-operations/index.md - [Variables and algebraic expressions](https://ocme.evemisslab.com/en/mko/mko-variable-expression/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-variable-expression/index.md - [Equation](https://ocme.evemisslab.com/en/mko/mko-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-equation/index.md - [Linear equation in one variable](https://ocme.evemisslab.com/en/mko/mko-linear-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-equation/index.md - [Set](https://ocme.evemisslab.com/en/mko/mko-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-set/index.md - [Proposition](https://ocme.evemisslab.com/en/mko/mko-proposition/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-proposition/index.md - [Logical connectives](https://ocme.evemisslab.com/en/mko/mko-logical-connectives/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-logical-connectives/index.md - [Mathematical proof](https://ocme.evemisslab.com/en/mko/mko-proof/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-proof/index.md - [Set membership](https://ocme.evemisslab.com/en/mko/mko-set-membership/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-set-membership/index.md - [Subset](https://ocme.evemisslab.com/en/mko/mko-subset/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-subset/index.md - [Set operations](https://ocme.evemisslab.com/en/mko/mko-set-operations/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-set-operations/index.md - [Sample space](https://ocme.evemisslab.com/en/mko/mko-sample-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-sample-space/index.md - [Event](https://ocme.evemisslab.com/en/mko/mko-event/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-event/index.md - [Function mapping](https://ocme.evemisslab.com/en/mko/mko-function-mapping/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-function-mapping/index.md - [Tends-to relation](https://ocme.evemisslab.com/en/mko/mko-tends-to-relation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-tends-to-relation/index.md - [Mathematical induction](https://ocme.evemisslab.com/en/mko/mko-mathematical-induction/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-mathematical-induction/index.md - [Basic counting principles](https://ocme.evemisslab.com/en/mko/mko-counting-principle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-counting-principle/index.md - [Factorial](https://ocme.evemisslab.com/en/mko/mko-factorial/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-factorial/index.md - [Absolute value](https://ocme.evemisslab.com/en/mko/mko-absolute-value/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-absolute-value/index.md - [Fraction](https://ocme.evemisslab.com/en/mko/mko-fraction/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-fraction/index.md - [Ratio and proportion](https://ocme.evemisslab.com/en/mko/mko-ratio-proportion/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-ratio-proportion/index.md - [Domain, codomain, and range](https://ocme.evemisslab.com/en/mko/mko-domain-codomain-range/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-domain-codomain-range/index.md - [Function composition](https://ocme.evemisslab.com/en/mko/mko-composition/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-composition/index.md - [Sequence](https://ocme.evemisslab.com/en/mko/mko-sequence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-sequence/index.md - [Permutations and combinations](https://ocme.evemisslab.com/en/mko/mko-permutation-combination/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-permutation-combination/index.md - [Coordinate plane](https://ocme.evemisslab.com/en/mko/mko-coordinate-plane/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-coordinate-plane/index.md - [Natural-number powers and principal square roots](https://ocme.evemisslab.com/en/mko/mko-power-root/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-power-root/index.md - [Univariate polynomials over the rationals](https://ocme.evemisslab.com/en/mko/mko-polynomial/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-polynomial/index.md - [Polynomial factorization over the rationals](https://ocme.evemisslab.com/en/mko/mko-factorization/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-factorization/index.md - [Quadratic equations over the reals](https://ocme.evemisslab.com/en/mko/mko-quadratic-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quadratic-equation/index.md - [Affine functions and degree-one functions](https://ocme.evemisslab.com/en/mko/mko-linear-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-function/index.md - [Graphs of real-valued functions](https://ocme.evemisslab.com/en/mko/mko-function-graph/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-function-graph/index.md - [Probability on finite sample spaces](https://ocme.evemisslab.com/en/mko/mko-probability/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-probability/index.md - [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/mko/mko-quantifier/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quantifier/index.md - [Counterexamples and domain eligibility](https://ocme.evemisslab.com/en/mko/mko-counterexample/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-counterexample/index.md - [Binary relations and set projections](https://ocme.evemisslab.com/en/mko/mko-relation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-relation/index.md - [Finite simple undirected graphs](https://ocme.evemisslab.com/en/mko/mko-graph/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-graph/index.md - [Plane vectors in a fixed basis](https://ocme.evemisslab.com/en/mko/mko-vector/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-vector/index.md - [Linear systems in two variables and degenerate constraints](https://ocme.evemisslab.com/en/mko/mko-system-linear-equations/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-system-linear-equations/index.md - [Conditional probability in finite models](https://ocme.evemisslab.com/en/mko/mko-conditional-probability/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-conditional-probability/index.md - [Injectivity and distinct inputs](https://ocme.evemisslab.com/en/mko/mko-injective/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-injective/index.md - [Surjectivity and codomain coverage](https://ocme.evemisslab.com/en/mko/mko-surjective/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-surjective/index.md - [Bijectivity and unique preimages](https://ocme.evemisslab.com/en/mko/mko-bijective/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bijective/index.md - [Inverse functions of bijections](https://ocme.evemisslab.com/en/mko/mko-inverse-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-inverse-function/index.md - [Real random variables on finite sample spaces](https://ocme.evemisslab.com/en/mko/mko-random-variable/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-random-variable/index.md - [Expectation in finite models](https://ocme.evemisslab.com/en/mko/mko-expectation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-expectation/index.md - [Variance in finite probability models](https://ocme.evemisslab.com/en/mko/mko-variance/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-variance/index.md - [Usual order on the real numbers](https://ocme.evemisslab.com/en/mko/mko-order-relation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-order-relation/index.md - [Quadratic functions in vertex form](https://ocme.evemisslab.com/en/mko/mko-quadratic-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quadratic-function/index.md - [Average rate of change between distinct inputs](https://ocme.evemisslab.com/en/mko/mko-rate-of-change/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-rate-of-change/index.md - [Euclidean distance in an equal-unit orthonormal frame](https://ocme.evemisslab.com/en/mko/mko-distance-formula/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-distance-formula/index.md - [Circle boundaries and zero-radius degeneracy](https://ocme.evemisslab.com/en/mko/mko-circle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-circle/index.md - [Exact area of half-open rectangles and unit-cell unions](https://ocme.evemisslab.com/en/mko/mko-area/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-area/index.md - [Descriptive summaries of nonempty observation lists](https://ocme.evemisslab.com/en/mko/mko-descriptive-statistics/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-descriptive-statistics/index.md - [Finite matrices: dimensions, indexing, and transpose](https://ocme.evemisslab.com/en/mko/mko-matrix/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-matrix/index.md - [Matrix-represented linear maps on the real plane](https://ocme.evemisslab.com/en/mko/mko-linear-transformation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-transformation/index.md - [Determinants of real 2×2 matrices](https://ocme.evemisslab.com/en/mko/mko-determinant/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-determinant/index.md - [Real eigenvalues and nonzero eigenvectors of 2×2 matrices](https://ocme.evemisslab.com/en/mko/mko-eigenvalue/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-eigenvalue/index.md - [Congruence of nondegenerate triangles with explicit correspondence](https://ocme.evemisslab.com/en/mko/mko-congruence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-congruence/index.md - [Labeled triangle similarity with a specified positive scale](https://ocme.evemisslab.com/en/mko/mko-similarity/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-similarity/index.md - [Plane-coordinate isometries and uniform scaling](https://ocme.evemisslab.com/en/mko/mko-geometric-transformations/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-geometric-transformations/index.md - [Sequence limits and exact tail cutoffs](https://ocme.evemisslab.com/en/mko/mko-sequence-limit/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-sequence-limit/index.md - [Function limits on punctured real domains](https://ocme.evemisslab.com/en/mko/mko-function-limit/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-function-limit/index.md - [Point values and continuity of real functions](https://ocme.evemisslab.com/en/mko/mko-continuity/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-continuity/index.md - [Real derivatives at a point and finite difference quotients](https://ocme.evemisslab.com/en/mko/mko-derivative/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-derivative/index.md - [Differentiating polynomial sums, products, and compositions](https://ocme.evemisslab.com/en/mko/mko-derivative-rules/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-derivative-rules/index.md - [Polynomial antiderivatives and the choice of constant](https://ocme.evemisslab.com/en/mko/mko-antiderivative/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-antiderivative/index.md - [Signed polynomial definite integrals on finite intervals](https://ocme.evemisslab.com/en/mko/mko-definite-integral/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-definite-integral/index.md - [Fundamental theorem of calculus: continuity and oriented endpoints](https://ocme.evemisslab.com/en/mko/mko-fundamental-theorem-calculus/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-fundamental-theorem-calculus/index.md - [Nonempty finite trees: connectivity, cycles, and unique paths](https://ocme.evemisslab.com/en/mko/mko-tree/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-tree/index.md - [Topological space](https://ocme.evemisslab.com/en/mko/mko-topological-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-space/index.md - [Natural-number divisibility](https://ocme.evemisslab.com/en/mko/mko-natural-divisibility/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-natural-divisibility/index.md - [Greatest common divisor and coprimality](https://ocme.evemisslab.com/en/mko/mko-gcd-coprime/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-gcd-coprime/index.md - [Prime natural number](https://ocme.evemisslab.com/en/mko/mko-prime-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-prime-number/index.md - [Natural-number congruence modulo a positive modulus](https://ocme.evemisslab.com/en/mko/mko-modular-congruence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-modular-congruence/index.md - [Decision problem](https://ocme.evemisslab.com/en/mko/mko-decision-problem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-decision-problem/index.md - [Formal statements in a proof assistant](https://ocme.evemisslab.com/en/mko/mko-lean-formal-statement/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-lean-formal-statement/index.md - [Open and closed sets](https://ocme.evemisslab.com/en/mko/mko-open-closed-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-open-closed-set/index.md - [Neighborhood](https://ocme.evemisslab.com/en/mko/mko-neighborhood/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-neighborhood/index.md - [Continuous maps between topological spaces](https://ocme.evemisslab.com/en/mko/mko-topological-continuity/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-continuity/index.md - [Abstract computational model](https://ocme.evemisslab.com/en/mko/mko-computational-model/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-computational-model/index.md - [Algorithm correctness](https://ocme.evemisslab.com/en/mko/mko-algorithm-correctness/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-algorithm-correctness/index.md - [Asymptotic resource bounds](https://ocme.evemisslab.com/en/mko/mko-asymptotic-resource-bound/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-asymptotic-resource-bound/index.md - [Proof term](https://ocme.evemisslab.com/en/mko/mko-lean-proof-term/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-lean-proof-term/index.md - [Discrete-time dynamical system](https://ocme.evemisslab.com/en/mko/mko-discrete-dynamical-system/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-discrete-dynamical-system/index.md - [Ordinary differential equation](https://ocme.evemisslab.com/en/mko/mko-ordinary-differential-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-ordinary-differential-equation/index.md - [Numerical approximation and error](https://ocme.evemisslab.com/en/mko/mko-numerical-approximation-error/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-numerical-approximation-error/index.md - [Optimization problem](https://ocme.evemisslab.com/en/mko/mko-optimization-problem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-optimization-problem/index.md - [Dimensional analysis](https://ocme.evemisslab.com/en/mko/mko-dimensional-analysis/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-dimensional-analysis/index.md - [Discrete exponential growth model](https://ocme.evemisslab.com/en/mko/mko-discrete-exponential-growth/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-discrete-exponential-growth/index.md - [Compound-interest model](https://ocme.evemisslab.com/en/mko/mko-compound-interest/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-compound-interest/index.md - [Mathematical representation](https://ocme.evemisslab.com/en/mko/mko-mathematical-representation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-mathematical-representation/index.md - [Diagnostic mathematical assessment records](https://ocme.evemisslab.com/en/mko/mko-diagnostic-mathematical-assessment/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-diagnostic-mathematical-assessment/index.md - [Orbits, fixed points and periodic points](https://ocme.evemisslab.com/en/mko/mko-orbit-fixed-periodic/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-orbit-fixed-periodic/index.md - [Initial-value problem](https://ocme.evemisslab.com/en/mko/mko-initial-value-problem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-initial-value-problem/index.md - [Finite sign-bracket updates in the bisection method](https://ocme.evemisslab.com/en/mko/mko-bisection-method/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bisection-method/index.md - [Linear programming](https://ocme.evemisslab.com/en/mko/mko-linear-programming/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-programming/index.md - [Discrete logistic increment model](https://ocme.evemisslab.com/en/mko/mko-discrete-logistic-growth/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-discrete-logistic-growth/index.md - [Linear harmonic-oscillator model](https://ocme.evemisslab.com/en/mko/mko-harmonic-oscillator-model/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-harmonic-oscillator-model/index.md - [Present value and discounting](https://ocme.evemisslab.com/en/mko/mko-present-value-discounting/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-present-value-discounting/index.md - [Complex number](https://ocme.evemisslab.com/en/mko/mko-complex-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-complex-number/index.md - [Real vector space](https://ocme.evemisslab.com/en/mko/mko-real-vector-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-vector-space/index.md - [Finite group](https://ocme.evemisslab.com/en/mko/mko-finite-group/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group/index.md - [Metric space](https://ocme.evemisslab.com/en/mko/mko-metric-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-metric-space/index.md - [Finite discrete probability distribution](https://ocme.evemisslab.com/en/mko/mko-finite-discrete-probability-distribution/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-discrete-probability-distribution/index.md - [Complex modulus and conjugation](https://ocme.evemisslab.com/en/mko/mko-complex-modulus-conjugate/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-complex-modulus-conjugate/index.md - [Linear combinations and span](https://ocme.evemisslab.com/en/mko/mko-linear-combination-span/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-combination-span/index.md - [Subgroups and group homomorphisms](https://ocme.evemisslab.com/en/mko/mko-subgroup-homomorphism/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-subgroup-homomorphism/index.md - [Convergence in a metric space](https://ocme.evemisslab.com/en/mko/mko-metric-convergence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-metric-convergence/index.md - [Sigma-algebras and measure spaces](https://ocme.evemisslab.com/en/mko/mko-sigma-algebra-measure-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-sigma-algebra-measure-space/index.md - [Discrete-time stochastic process](https://ocme.evemisslab.com/en/mko/mko-discrete-stochastic-process/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-discrete-stochastic-process/index.md - [Multivariable real-valued function](https://ocme.evemisslab.com/en/mko/mko-multivariable-real-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-multivariable-real-function/index.md - [Linear independence and bases](https://ocme.evemisslab.com/en/mko/mko-linear-independence-basis/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-independence-basis/index.md - [Measurable function](https://ocme.evemisslab.com/en/mko/mko-measurable-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-measurable-function/index.md - [Finite-state Markov chain](https://ocme.evemisslab.com/en/mko/mko-finite-markov-chain/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-markov-chain/index.md - [Partial derivative](https://ocme.evemisslab.com/en/mko/mko-partial-derivative/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-partial-derivative/index.md - [Finite convex combination](https://ocme.evemisslab.com/en/mko/mko-finite-convex-combination/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-convex-combination/index.md - [Partial differential equation](https://ocme.evemisslab.com/en/mko/mko-partial-differential-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-partial-differential-equation/index.md - [Convex set](https://ocme.evemisslab.com/en/mko/mko-convex-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-convex-set/index.md - [Boundary-value problem](https://ocme.evemisslab.com/en/mko/mko-boundary-value-problem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-boundary-value-problem/index.md - [Convex function](https://ocme.evemisslab.com/en/mko/mko-convex-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-convex-function/index.md - [Convex optimization problem](https://ocme.evemisslab.com/en/mko/mko-convex-optimization-problem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-convex-optimization-problem/index.md - [Finite abelian group](https://ocme.evemisslab.com/en/mko/mko-finite-abelian-group/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-abelian-group/index.md - [Real normed vector space](https://ocme.evemisslab.com/en/mko/mko-real-normed-vector-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-normed-vector-space/index.md - [Cauchy sequence](https://ocme.evemisslab.com/en/mko/mko-cauchy-sequence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-cauchy-sequence/index.md - [Finite joint distribution](https://ocme.evemisslab.com/en/mko/mko-finite-joint-distribution/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-joint-distribution/index.md - [Covariance](https://ocme.evemisslab.com/en/mko/mko-covariance/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-covariance/index.md - [Graph isomorphism](https://ocme.evemisslab.com/en/mko/mko-graph-isomorphism/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-graph-isomorphism/index.md - [Equivalence relation](https://ocme.evemisslab.com/en/mko/mko-equivalence-relation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-equivalence-relation/index.md - [Finite unital ring](https://ocme.evemisslab.com/en/mko/mko-finite-unital-ring/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-unital-ring/index.md - [Norm-induced metric](https://ocme.evemisslab.com/en/mko/mko-norm-induced-metric/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-norm-induced-metric/index.md - [Complete metric space](https://ocme.evemisslab.com/en/mko/mko-complete-metric-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-complete-metric-space/index.md - [Real bilinear form](https://ocme.evemisslab.com/en/mko/mko-real-bilinear-form/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-bilinear-form/index.md - [Linear map between real vector spaces](https://ocme.evemisslab.com/en/mko/mko-general-linear-map/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-general-linear-map/index.md - [Event independence](https://ocme.evemisslab.com/en/mko/mko-event-independence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-event-independence/index.md - [Graph walks and simple paths](https://ocme.evemisslab.com/en/mko/mko-graph-walk-simple-path/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-graph-walk-simple-path/index.md - [Finite commutative ring](https://ocme.evemisslab.com/en/mko/mko-finite-commutative-ring/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-commutative-ring/index.md - [Finite two-sided ideal](https://ocme.evemisslab.com/en/mko/mko-finite-two-sided-ideal/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-two-sided-ideal/index.md - [Real Banach space](https://ocme.evemisslab.com/en/mko/mko-real-banach-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-banach-space/index.md - [Real inner-product space](https://ocme.evemisslab.com/en/mko/mko-real-inner-product-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-inner-product-space/index.md - [Bounded linear operator](https://ocme.evemisslab.com/en/mko/mko-bounded-linear-operator/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bounded-linear-operator/index.md - [Independence of random variables](https://ocme.evemisslab.com/en/mko/mko-random-variable-independence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-random-variable-independence/index.md - [Connected component](https://ocme.evemisslab.com/en/mko/mko-connected-component/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-connected-component/index.md - [Finite integral domain](https://ocme.evemisslab.com/en/mko/mko-finite-integral-domain/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-integral-domain/index.md - [Polynomial ring over a finite commutative ring](https://ocme.evemisslab.com/en/mko/mko-polynomial-ring-over-finite-commutative-ring/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-polynomial-ring-over-finite-commutative-ring/index.md - [Inner-product-induced norm](https://ocme.evemisslab.com/en/mko/mko-inner-product-induced-norm/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-inner-product-induced-norm/index.md - [Finite conditional expectation](https://ocme.evemisslab.com/en/mko/mko-conditional-expectation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-conditional-expectation/index.md - [Finite filtration](https://ocme.evemisslab.com/en/mko/mko-finite-filtration/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-filtration/index.md - [Independent identically distributed sequence](https://ocme.evemisslab.com/en/mko/mko-iid-sequence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-iid-sequence/index.md - [Equivalence class](https://ocme.evemisslab.com/en/mko/mko-equivalence-class/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-equivalence-class/index.md - [Finite field](https://ocme.evemisslab.com/en/mko/mko-finite-field/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-field/index.md - [Real Hilbert space](https://ocme.evemisslab.com/en/mko/mko-real-hilbert-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-hilbert-space/index.md - [Finite martingale](https://ocme.evemisslab.com/en/mko/mko-martingale/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-martingale/index.md - [Quotient set](https://ocme.evemisslab.com/en/mko/mko-quotient-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quotient-set/index.md - [Cardinality comparison of sets](https://ocme.evemisslab.com/en/mko/mko-cardinality-comparison/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-cardinality-comparison/index.md - [Cumulative distribution function](https://ocme.evemisslab.com/en/mko/mko-cumulative-distribution-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-cumulative-distribution-function/index.md - [Convergence in probability](https://ocme.evemisslab.com/en/mko/mko-convergence-in-probability/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-convergence-in-probability/index.md - [At-most-countable set](https://ocme.evemisslab.com/en/mko/mko-at-most-countable-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-at-most-countable-set/index.md - [Bipartite graph](https://ocme.evemisslab.com/en/mko/mko-bipartite-graph/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bipartite-graph/index.md - [Convergence in distribution](https://ocme.evemisslab.com/en/mko/mko-convergence-in-distribution/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-convergence-in-distribution/index.md - [Quotient ring of a finite ring](https://ocme.evemisslab.com/en/mko/mko-finite-quotient-ring/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-quotient-ring/index.md - [Graph coloring](https://ocme.evemisslab.com/en/mko/mko-graph-coloring/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-graph-coloring/index.md - [Real vector subspace](https://ocme.evemisslab.com/en/mko/mko-vector-subspace/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-vector-subspace/index.md - [Topological closure and interior](https://ocme.evemisslab.com/en/mko/mko-closure-and-interior/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-closure-and-interior/index.md - [Open cover and subcover](https://ocme.evemisslab.com/en/mko/mko-open-cover-and-subcover/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-open-cover-and-subcover/index.md - [Almost-sure convergence](https://ocme.evemisslab.com/en/mko/mko-almost-sure-convergence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-almost-sure-convergence/index.md - [Graph matching](https://ocme.evemisslab.com/en/mko/mko-graph-matching/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-graph-matching/index.md - [Euler totient function](https://ocme.evemisslab.com/en/mko/mko-euler-totient-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euler-totient-function/index.md - [Deterministic finite automaton](https://ocme.evemisslab.com/en/mko/mko-finite-automaton/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-automaton/index.md - [Dimension of a finite-dimensional vector space](https://ocme.evemisslab.com/en/mko/mko-vector-space-dimension/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-vector-space-dimension/index.md - [Kernel of a linear map](https://ocme.evemisslab.com/en/mko/mko-linear-map-kernel/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-map-kernel/index.md - [Image of a linear map](https://ocme.evemisslab.com/en/mko/mko-linear-map-image/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-map-image/index.md - [Topological boundary](https://ocme.evemisslab.com/en/mko/mko-topological-boundary/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-boundary/index.md - [Compact topological space](https://ocme.evemisslab.com/en/mko/mko-compact-topological-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-compact-topological-space/index.md - [Bayes theorem](https://ocme.evemisslab.com/en/mko/mko-bayes-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bayes-theorem/index.md - [Regular language](https://ocme.evemisslab.com/en/mko/mko-regular-language/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-regular-language/index.md - [Matrix rank](https://ocme.evemisslab.com/en/mko/mko-matrix-rank/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-matrix-rank/index.md - [Pointwise convergence of functions](https://ocme.evemisslab.com/en/mko/mko-pointwise-convergence-of-functions/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-pointwise-convergence-of-functions/index.md - [Infinite series](https://ocme.evemisslab.com/en/mko/mko-infinite-series/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-infinite-series/index.md - [Parametric statistical model](https://ocme.evemisslab.com/en/mko/mko-parametric-statistical-model/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-parametric-statistical-model/index.md - [Connected topological space](https://ocme.evemisslab.com/en/mko/mko-connected-topological-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-connected-topological-space/index.md - [Maximum matching](https://ocme.evemisslab.com/en/mko/mko-maximum-matching/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-maximum-matching/index.md - [Modular inverse](https://ocme.evemisslab.com/en/mko/mko-modular-inverse/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-modular-inverse/index.md - [Rank-nullity theorem](https://ocme.evemisslab.com/en/mko/mko-rank-nullity-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-rank-nullity-theorem/index.md - [Uniform convergence of functions](https://ocme.evemisslab.com/en/mko/mko-uniform-convergence-of-functions/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-uniform-convergence-of-functions/index.md - [Absolute convergence of series](https://ocme.evemisslab.com/en/mko/mko-absolute-convergence-of-series/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-absolute-convergence-of-series/index.md - [Statistical estimator](https://ocme.evemisslab.com/en/mko/mko-statistical-estimator/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-statistical-estimator/index.md - [Chinese remainder theorem](https://ocme.evemisslab.com/en/mko/mko-chinese-remainder-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-chinese-remainder-theorem/index.md - [Spanning tree](https://ocme.evemisslab.com/en/mko/mko-spanning-tree/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-spanning-tree/index.md - [Lp convergence](https://ocme.evemisslab.com/en/mko/mko-lp-convergence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-lp-convergence/index.md - [Direct sum of subspaces](https://ocme.evemisslab.com/en/mko/mko-direct-sum/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-direct-sum/index.md - [Dual vector space](https://ocme.evemisslab.com/en/mko/mko-dual-vector-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-dual-vector-space/index.md - [Euclidean algorithm](https://ocme.evemisslab.com/en/mko/mko-euclidean-algorithm/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euclidean-algorithm/index.md - [Euler trails and circuits](https://ocme.evemisslab.com/en/mko/mko-eulerian-trail/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-eulerian-trail/index.md - [Homeomorphism](https://ocme.evemisslab.com/en/mko/mko-homeomorphism/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-homeomorphism/index.md - [Sampling distribution](https://ocme.evemisslab.com/en/mko/mko-sampling-distribution/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-sampling-distribution/index.md - [Weak law of large numbers](https://ocme.evemisslab.com/en/mko/mko-weak-law-large-numbers/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-weak-law-large-numbers/index.md - [Chromatic number](https://ocme.evemisslab.com/en/mko/mko-chromatic-number/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-chromatic-number/index.md - [Cliques and independent sets](https://ocme.evemisslab.com/en/mko/mko-clique-and-independent-set/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-clique-and-independent-set/index.md - [Estimator bias](https://ocme.evemisslab.com/en/mko/mko-estimator-bias/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-estimator-bias/index.md - [Estimator variance](https://ocme.evemisslab.com/en/mko/mko-estimator-variance/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-estimator-variance/index.md - [Fermat's little theorem](https://ocme.evemisslab.com/en/mko/mko-fermat-little-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-fermat-little-theorem/index.md - [Linear Diophantine equation](https://ocme.evemisslab.com/en/mko/mko-linear-diophantine-equation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-diophantine-equation/index.md - [Quotient vector space](https://ocme.evemisslab.com/en/mko/mko-quotient-vector-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quotient-vector-space/index.md - [Finite group action](https://ocme.evemisslab.com/en/mko/mko-finite-group-action/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-action/index.md - [Supremum and infimum](https://ocme.evemisslab.com/en/mko/mko-supremum-and-infimum/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-supremum-and-infimum/index.md - [Topological basis](https://ocme.evemisslab.com/en/mko/mko-topological-basis/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-basis/index.md - [Markov inequality](https://ocme.evemisslab.com/en/mko/mko-markov-inequality/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-markov-inequality/index.md - [Pigeonhole principle](https://ocme.evemisslab.com/en/mko/mko-pigeonhole-principle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-pigeonhole-principle/index.md - [Euler's theorem in number theory](https://ocme.evemisslab.com/en/mko/mko-euler-theorem-number-theory/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euler-theorem-number-theory/index.md - [Subsequence](https://ocme.evemisslab.com/en/mko/mko-subsequence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-subsequence/index.md - [Orbit of a finite group action](https://ocme.evemisslab.com/en/mko/mko-finite-group-orbit/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-orbit/index.md - [Monotone bounded sequence convergence theorem](https://ocme.evemisslab.com/en/mko/mko-monotone-sequence-convergence-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-monotone-sequence-convergence-theorem/index.md - [Subspace topology](https://ocme.evemisslab.com/en/mko/mko-subspace-topology/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-subspace-topology/index.md - [Chebyshev inequality](https://ocme.evemisslab.com/en/mko/mko-chebyshev-inequality/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-chebyshev-inequality/index.md - [Inclusion-exclusion principle](https://ocme.evemisslab.com/en/mko/mko-inclusion-exclusion-principle/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-inclusion-exclusion-principle/index.md - [Unique prime factorization of integers](https://ocme.evemisslab.com/en/mko/mko-unique-prime-factorization/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-unique-prime-factorization/index.md - [Finite directed graph](https://ocme.evemisslab.com/en/mko/mko-finite-directed-graph/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-directed-graph/index.md - [Stabilizer of a finite group action](https://ocme.evemisslab.com/en/mko/mko-finite-group-stabilizer/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-stabilizer/index.md - [Bolzano-Weierstrass theorem for real sequences](https://ocme.evemisslab.com/en/mko/mko-bolzano-weierstrass-theorem-real/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bolzano-weierstrass-theorem-real/index.md - [Compact subset](https://ocme.evemisslab.com/en/mko/mko-compact-subset/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-compact-subset/index.md - [Law of total expectation](https://ocme.evemisslab.com/en/mko/mko-law-of-total-expectation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-law-of-total-expectation/index.md - [Binomial theorem](https://ocme.evemisslab.com/en/mko/mko-binomial-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-binomial-theorem/index.md - [Mobius function](https://ocme.evemisslab.com/en/mko/mko-mobius-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-mobius-function/index.md - [Context-free grammar](https://ocme.evemisslab.com/en/mko/mko-context-free-grammar/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-context-free-grammar/index.md - [Orbit-stabilizer theorem](https://ocme.evemisslab.com/en/mko/mko-orbit-stabilizer-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-orbit-stabilizer-theorem/index.md - [Mean value theorem](https://ocme.evemisslab.com/en/mko/mko-mean-value-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-mean-value-theorem/index.md - [Continuous image of a compact set](https://ocme.evemisslab.com/en/mko/mko-continuous-image-of-compact/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-continuous-image-of-compact/index.md - [Law of total variance](https://ocme.evemisslab.com/en/mko/mko-law-of-total-variance/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-law-of-total-variance/index.md - [Recurrence relation](https://ocme.evemisslab.com/en/mko/mko-recurrence-relation/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-recurrence-relation/index.md - [Mobius inversion on finite divisor sets](https://ocme.evemisslab.com/en/mko/mko-mobius-inversion-finite-divisors/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-mobius-inversion-finite-divisors/index.md - [Pushdown automaton](https://ocme.evemisslab.com/en/mko/mko-pushdown-automaton/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-pushdown-automaton/index.md - [Lagrange theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-lagrange-theorem-finite-groups/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-lagrange-theorem-finite-groups/index.md - [Higher-order derivative](https://ocme.evemisslab.com/en/mko/mko-higher-order-derivative/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-higher-order-derivative/index.md - [Hausdorff space](https://ocme.evemisslab.com/en/mko/mko-hausdorff-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-hausdorff-space/index.md - [Continuous real distribution function](https://ocme.evemisslab.com/en/mko/mko-continuous-real-distribution-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-continuous-real-distribution-function/index.md - [Catalan numbers](https://ocme.evemisslab.com/en/mko/mko-catalan-numbers/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-catalan-numbers/index.md - [Quadratic residue](https://ocme.evemisslab.com/en/mko/mko-quadratic-residue/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quadratic-residue/index.md - [Nondeterministic finite automaton](https://ocme.evemisslab.com/en/mko/mko-nondeterministic-finite-automaton/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-nondeterministic-finite-automaton/index.md - [Cauchy theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-cauchy-theorem-finite-groups/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-cauchy-theorem-finite-groups/index.md - [Taylor polynomial](https://ocme.evemisslab.com/en/mko/mko-taylor-polynomial/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-taylor-polynomial/index.md - [A compact subset of a Hausdorff space is closed](https://ocme.evemisslab.com/en/mko/mko-compact-subset-closed-in-hausdorff/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-compact-subset-closed-in-hausdorff/index.md - [Improper integral](https://ocme.evemisslab.com/en/mko/mko-improper-integral/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-improper-integral/index.md - [Radius of convergence of a power series](https://ocme.evemisslab.com/en/mko/mko-power-series-radius-of-convergence/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-power-series-radius-of-convergence/index.md - [Legendre symbol](https://ocme.evemisslab.com/en/mko/mko-legendre-symbol/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-legendre-symbol/index.md - [Subset construction from an NFA to a DFA](https://ocme.evemisslab.com/en/mko/mko-subset-construction-nfa-to-dfa/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-subset-construction-nfa-to-dfa/index.md - [Finite normal subgroup](https://ocme.evemisslab.com/en/mko/mko-finite-normal-subgroup/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-normal-subgroup/index.md - [Real exponential function](https://ocme.evemisslab.com/en/mko/mko-real-exponential-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-real-exponential-function/index.md - [Analytic ordinary generating function](https://ocme.evemisslab.com/en/mko/mko-analytic-ordinary-generating-function/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-analytic-ordinary-generating-function/index.md - [Euler criterion for quadratic residues](https://ocme.evemisslab.com/en/mko/mko-euler-criterion-quadratic-residue/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-euler-criterion-quadratic-residue/index.md - [Turing-machine decision model](https://ocme.evemisslab.com/en/mko/mko-turing-machine-decision-model/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-turing-machine-decision-model/index.md - [Gradient vector](https://ocme.evemisslab.com/en/mko/mko-gradient-vector/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-gradient-vector/index.md - [Finite flow network](https://ocme.evemisslab.com/en/mko/mko-finite-flow-network/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-flow-network/index.md - [Kernel of a finite group homomorphism](https://ocme.evemisslab.com/en/mko/mko-finite-group-homomorphism-kernel/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-homomorphism-kernel/index.md - [Finite quotient group](https://ocme.evemisslab.com/en/mko/mko-finite-quotient-group/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-quotient-group/index.md - [Conjugacy class in a finite group](https://ocme.evemisslab.com/en/mko/mko-finite-group-conjugacy-class/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-conjugacy-class/index.md - [Standard normal distribution](https://ocme.evemisslab.com/en/mko/mko-standard-normal-distribution/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-standard-normal-distribution/index.md - [Mean squared error of an estimator](https://ocme.evemisslab.com/en/mko/mko-estimator-mean-squared-error/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-estimator-mean-squared-error/index.md - [Standard form of a linear program](https://ocme.evemisslab.com/en/mko/mko-linear-program-standard-form/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-program-standard-form/index.md - [Vertex cover](https://ocme.evemisslab.com/en/mko/mko-vertex-cover/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-vertex-cover/index.md - [First isomorphism theorem for finite groups](https://ocme.evemisslab.com/en/mko/mko-first-isomorphism-theorem-finite-groups/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-first-isomorphism-theorem-finite-groups/index.md - [Center of a finite group](https://ocme.evemisslab.com/en/mko/mko-finite-group-center/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-center/index.md - [Bias-variance decomposition](https://ocme.evemisslab.com/en/mko/mko-bias-variance-decomposition/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-bias-variance-decomposition/index.md - [Linear-programming duality](https://ocme.evemisslab.com/en/mko/mko-linear-program-duality/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-linear-program-duality/index.md - [Max-flow min-cut theorem](https://ocme.evemisslab.com/en/mko/mko-max-flow-min-cut-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-max-flow-min-cut-theorem/index.md - [Minimum vertex cover](https://ocme.evemisslab.com/en/mko/mko-minimum-vertex-cover/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-minimum-vertex-cover/index.md - [Many-one reduction](https://ocme.evemisslab.com/en/mko/mko-many-one-reduction/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-many-one-reduction/index.md - [Contraction mapping theorem](https://ocme.evemisslab.com/en/mko/mko-contraction-mapping-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-contraction-mapping-theorem/index.md - [Intermediate value theorem](https://ocme.evemisslab.com/en/mko/mko-intermediate-value-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-intermediate-value-theorem/index.md - [Taylor remainder theorem](https://ocme.evemisslab.com/en/mko/mko-taylor-remainder-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-taylor-remainder-theorem/index.md - [Maximum-likelihood estimator in a finite model](https://ocme.evemisslab.com/en/mko/mko-finite-maximum-likelihood-estimator/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-maximum-likelihood-estimator/index.md - [Sufficient statistic in a finite model](https://ocme.evemisslab.com/en/mko/mko-finite-sufficient-statistic/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-sufficient-statistic/index.md - [Topological ordering of a directed acyclic graph](https://ocme.evemisslab.com/en/mko/mko-topological-ordering-dag/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-ordering-dag/index.md - [Multiplicative order modulo n](https://ocme.evemisslab.com/en/mko/mko-multiplicative-order-mod-n/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-multiplicative-order-mod-n/index.md - [Comparison tests for series](https://ocme.evemisslab.com/en/mko/mko-series-comparison-test/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-series-comparison-test/index.md - [Ratio test for series](https://ocme.evemisslab.com/en/mko/mko-ratio-test-series/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-ratio-test-series/index.md - [A uniform limit of continuous functions is continuous](https://ocme.evemisslab.com/en/mko/mko-uniform-limit-continuity-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-uniform-limit-continuity-theorem/index.md - [Finite product topology](https://ocme.evemisslab.com/en/mko/mko-finite-product-topology/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-product-topology/index.md - [Quotient topology](https://ocme.evemisslab.com/en/mko/mko-quotient-topology/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-quotient-topology/index.md - [Path-connected space](https://ocme.evemisslab.com/en/mko/mko-path-connected-space/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-path-connected-space/index.md - [Connected component of a topological space](https://ocme.evemisslab.com/en/mko/mko-topological-connected-component/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-topological-connected-component/index.md - [Central limit theorem for finite-variance IID sequences](https://ocme.evemisslab.com/en/mko/mko-central-limit-theorem-finite-variance-iid/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-central-limit-theorem-finite-variance-iid/index.md - [Strong law of large numbers for finite-valued IID sequences](https://ocme.evemisslab.com/en/mko/mko-strong-law-large-numbers-finite-valued-iid/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-strong-law-large-numbers-finite-valued-iid/index.md - [Confidence-interval coverage in a finite model](https://ocme.evemisslab.com/en/mko/mko-finite-confidence-interval-coverage/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-confidence-interval-coverage/index.md - [Wilson theorem](https://ocme.evemisslab.com/en/mko/mko-wilson-theorem/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-wilson-theorem/index.md - [p-adic valuation of integers](https://ocme.evemisslab.com/en/mko/mko-p-adic-valuation-integers/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-p-adic-valuation-integers/index.md - [Regular expression](https://ocme.evemisslab.com/en/mko/mko-regular-expression/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-regular-expression/index.md - [Pumping lemma for regular languages](https://ocme.evemisslab.com/en/mko/mko-pumping-lemma-regular-languages/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-pumping-lemma-regular-languages/index.md - [Newton method for root finding](https://ocme.evemisslab.com/en/mko/mko-newton-method/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-newton-method/index.md - [Composite trapezoidal quadrature](https://ocme.evemisslab.com/en/mko/mko-trapezoidal-quadrature/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-trapezoidal-quadrature/index.md - [Gradient descent](https://ocme.evemisslab.com/en/mko/mko-gradient-descent/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-gradient-descent/index.md - [Necessary Lagrange multiplier condition for equality constraints](https://ocme.evemisslab.com/en/mko/mko-lagrange-multiplier-condition/index.md): zh-Hant https://ocme.evemisslab.com/zh-Hant/mko/mko-lagrange-multiplier-condition/index.md ## Structured data - [Canonical object index](https://ocme.evemisslab.com/data/index.json) - [Question batch index](https://ocme.evemisslab.com/data/questions/index.json) - [Evidence index](https://ocme.evemisslab.com/data/evidence/index.json) - [Source-bound presentation field orders](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)