“ProofThatAFiniteCollectionOfSetsWillNotSuffice”的概念、定义、习题解题方法及翻译-数学辞典

单词	ProofThatAFiniteCollectionOfSetsWillNotSuffice
释义	proof that a finite collection of sets will not suffice Suppose that you cut $[0,1]$ into $A_{0},...,A_{n}$ .Displacing the parts is simply translating them; you can supposethat you leave $A_{0}$ in place and translate all the others to theright. Let $\\epsilon$ be the smallest translation length : if aftertranslation the union contains $[0,1]$ , necessarily $[0,\\epsilon]\\subset A_{0}$ . A contradiction ensues.
随便看	3.6 The logic of mere propositions 37PropositionalTruncation 3.7 Propositional truncation 38TheAxiomOfChoice 3.8 The axiom of choice 39ThePrincipleOfUniqueChoice 3.9 The principle of unique choice 3DistributedDynamicalSystems 3. Distributed dynamical systems 3manifold 3-manifold 3-manifold 3manifold1 41Quasiinverses 4.1 Quasi-inverses 42HalfAdjointEquivalences 4.2 Half adjoint equivalences 43BiinvertibleMaps 4.3 Bi-invertible maps 44ContractibleFibers 4.4 Contractible fibers 45OnTheDefinitionOfEquivalences 4.5 On the definition of equivalences 46SurjectionsAndEmbeddings 4.6 Surjections and embeddings

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proof that a finite collection of sets will not suffice