OCME · Bilingual mathematics & derivations

Question batches

36,000 questions have bilingual step-by-step derivations. Browse original batches or search and filter in the question explorer.

Search all questions & derivations →

Question batch · 100 questions

Explicit Finite Discrete Dynamics and Invariant Subsets

Discrete-time dynamical system

batch-20261013-advance-20261020-r01-discrete-dynamical-system-foundations

Question batch · 100 questions

Synthetic Proof Terms and Receipt Obligations, Not Lean Execution

Proof term

batch-20261013-advance-20261019-r07-lean-proof-term-foundations

Question batch · 100 questions

Explicit Full-Tail Resource Bounds versus Finite Benchmarks

Asymptotic resource bounds

batch-20261013-advance-20261019-r06-asymptotic-resource-bound-foundations

Question batch · 100 questions

Partial Correctness, Ranking Obligations, and All-Path Termination

Algorithm correctness

batch-20261013-advance-20261019-r05-algorithm-correctness-foundations

Question batch · 100 questions

Finite Transition Models, Halt Truncation, and Stuck States

Abstract computational model

batch-20261013-advance-20261019-r04-computational-model-foundations

Question batch · 100 questions

Complete Open-Preimage Continuity and Open-Map Contrasts

Continuous maps between topological spaces

batch-20261013-advance-20261019-r03-topological-continuity-foundations

Question batch · 100 questions

Point-Qualified Neighborhoods and All Open Witnesses

Neighborhood

batch-20261013-advance-20261019-r02-neighborhood-foundations

Question batch · 100 questions

Open, Closed, and Clopen Sets in Complete Finite Topologies

Open and closed sets

batch-20261013-advance-20261019-r01-open-closed-set-foundations

Question batch · 100 questions

Synthetic Formal-Statement Pipeline Records, Not Lean Execution

Formal statements in a proof assistant

batch-20261013-advance-20261018-r07-lean-formal-statement-foundations

Question batch · 100 questions

Finite Decision Specifications versus Complete and Sampled Tables

Decision problem

batch-20261013-advance-20261018-r06-decision-problem-foundations

Question batch · 100 questions

Positive-Modulus Natural Congruence and Guarded Preservation

Natural-number congruence modulo a positive modulus

batch-20261013-advance-20261018-r05-modular-congruence-foundations

Question batch · 100 questions

Prime Natural Numbers and Complete Factor Checks

Prime natural number

batch-20261013-advance-20261018-r04-prime-number-foundations

Question batch · 100 questions

Natural GCD, Euclid Traces, and Coprimality

Greatest common divisor and coprimality

batch-20261013-advance-20261018-r03-gcd-coprime-foundations

Question batch · 100 questions

Natural Divisibility, Explicit Witnesses, and Zero Boundaries

Natural-number divisibility

batch-20261013-advance-20261018-r02-natural-divisibility-foundations

Question batch · 100 questions

Complete Finite Topology Axioms and Open-Set Inventories

Topological space

batch-20261013-advance-20261018-r01-topological-space-foundations

Question batch · 100 questions

Finite-Domain Counterexamples and Explicit Predicate Extensions

Counterexamples and domain eligibility

batch-20261012-advance-20261017-r07-counterexample-foundations

Question batch · 100 questions

Nonempty Tree Qualification, Paths, Leaves, and New-Edge Cycles

Nonempty finite trees: connectivity, cycles, and unique paths

batch-20261012-advance-20261017-r06-tree-foundations

Question batch · 100 questions

Simple Undirected Graph Inventories and Induced Subsets

Finite simple undirected graphs

batch-20261012-advance-20261017-r05-graph-foundations

Question batch · 100 questions

Exact Rational Order and Closed-Interval Boundaries

Usual order on the real numbers

batch-20261012-advance-20261017-r04-order-relation-foundations

Question batch · 100 questions

Typed Relations, Projections, and Totality Guards

Binary relations and set projections

batch-20261012-advance-20261017-r03-relation-foundations

Question batch · 100 questions

Inverse Existence, Whole-Table Types, and Two-Sided Identities

Inverse functions of bijections

batch-20261012-advance-20261017-r02-inverse-function-foundations

Question batch · 100 questions

Complete Finite-Map Bijections and Cardinality Guards

Bijectivity and unique preimages

batch-20261012-advance-20261017-r01-bijective-foundations

Question batch · 100 questions

Declared Codomain Fibers, Changes, and Target Guards

Surjectivity and codomain coverage

batch-20261012-advance-20261016-r07-surjective-foundations

Question batch · 100 questions

Complete Finite-Map Collisions and Original Source Labels

Injectivity and distinct inputs

batch-20261012-advance-20261016-r06-injective-foundations