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

单词	PartitionsLessThanCofinality
释义	partitions less than cofinality If $\\lambda<\\operatorname{cf}(\\kappa)$ then $\\kappa\\rightarrow(\\kappa)^{1}_{\\lambda}$ . This follows easily from the definition of cofinality. For any coloring $f:\\kappa\\rightarrow\\lambda$ then define $g:\\lambda\\rightarrow\\kappa+1$ by $g(\\alpha)=\|f^{-1}(\\alpha)\|$ . Then $\\kappa=\\sum_{\\alpha<\\lambda}g(\\alpha)$ , and by the normal rules of cardinal arithmetic $\\operatorname{sup}_{\\alpha<\\lambda}g(\\alpha)=\\kappa$ . Since $\\lambda<\\operatorname{cf}(\\kappa)$ , there must be some $\\alpha<\\lambda$ such that $g(\\alpha)=\\kappa$ .
随便看	existence and uniqueness of compact real form ExistenceAndUniquenessOfDecimalExpansion existence and uniqueness of decimal expansion ExistenceAndUniquenessOfSolutionOfOrdinaryDifferentialEquations existence and uniqueness of solution of ordinary differential equations ExistenceAndUniquenessOfSolutionToCauchyProblem existence and uniqueness of solution to Cauchy problem ExistenceAndUniquenessOfTheGcdOfTwoIntegers existence and uniqueness of the gcd of two integers ExistenceOfAdjointsOfBoundedOperators existence of adjoints of bounded operators ExistenceOfExtensionsOfFieldIsomorphismsToSplittingFields existence of extensions of field isomorphisms to splitting fields ExistenceOfHilbertClassField existence of Hilbert class field ExistenceOfLaplaceTransform existence of Laplace transform ExistenceOfMaximalIdeals existence of maximal ideals ExistenceOfMaximalSemilatticeDecomposition existence of maximal semilattice decomposition ExistenceOfMaximalSubgroups existence of maximal subgroups ExistenceOfNthRoot existence of nth root

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

partitions less than cofinality