Counterexample


A counterexample is any exception to a universal generalization. It is an element of the domain for which a predicate is false. A single counterexample can disprove a universal statement.

Logic & Proofs
IntegerRational numberInequalityReal numberTheoremProofStatementProof by exhaustionUniversal generalizationCounterexampleExistence proofExistential instantiationAxiomLogicTruthPropositionCompound propositionLogical operationLogical equivalenceTautologyContradictionLogic lawPredicateDomainQuantifierArgumentRule of inferenceLogical proofDirect proofProof by contrapositiveIrrational numberProof by contradictionProof by casesSummationDisjunctive normal form
Set Theory
SetElementEmpty setUniversal setSubsetPower setCartesian productStringBinary stringEmpty stringSet operationSet identitySet proof
Functions
FunctionFloor functionCeiling functionInverse function
Algorithms
AlgorithmPseudocodeCommandAsymptotic notationTime complexityAtomic operationBrute-force algorithm
Relations
RelationReflexive relationSymmetric relationTransitive relationRelation compositionEquivalence relationEquivalence class
Number Theory
Integer divisionLinear combinationDivision algorithmModular arithmeticPrime factorizationGreatest common divisorLeast common multiplePrimality testFactoring algorithmEuclid's theoremPrime number theoremEuclidean algorithm
Induction
Proof by inductionFibonacci sequenceProof by strong inductionWell-ordering principleSequenceFactorialRecursive definition
Combinatorics
Rule of productRule of sumBijection rulePermutationCombinationComplement ruleExperimentOutcomeSample spaceEventProbabilityProbability distributionUniform distributionMultisetSixfold wayInclusion-exclusion principlePigeonhole principle
Graph Theory
GraphWalkSubgraphRegular graphComplete graphEmpty graphCycle graphHypercube graphBipartite graphComponentEulerian circuitEulerian trailHamiltonian cycleHamiltonian pathTreeHuffman treeSubstringForestPath graphStarSpanning treeWeighted graphMinimum spanning treeGreedy algorithmPrim's algorithm
Recursion
RecursionRecursive algorithmCorrectness proofDivide-and-conquer algorithmSorting algorithmMerge sort