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

单词	ConvergenceOfASequenceWithFiniteUpcrossings
释义	convergence of a sequence with finite upcrossings The following result characterizes convergence of a sequence in terms of finiteness of numbers of upcrossings. Theorem. A sequence $x_{1},x_{2},\\ldots$ of real numbers converges to a limit in the extended real numbers if and only if the number of upcrossings $U[a,b]$ is finite for all $a<b$ . Since the number of upcrossings $U[a,b]$ differs from the number of downcrossings $D[a,b]$ by at most one, the theorem can equivalently be stated in terms of the finiteness of $D[a,b]$ .
随便看	ExampleOfTaylorPolynomialsForTheExponentialFunction example of Taylor polynomials for the exponential function ExampleOfTelescopingSum example of telescoping sum ExampleOfTestsForLocalExtremaInLagrangeMultiplierMethod example of tests for local extrema in Lagrange multiplier method ExampleOfTraceOfAMatrix example of trace of a matrix ExampleOfTranscendentalNumber example of transcendental number ExampleOfTransfiniteInduction example of transfinite induction ExampleOfTreesetTheoretic example of tree (set theoretic) ExampleOfUncountableFamilyOfSubsetsOfACountableSetWithFiniteIntersections example of uncountable family of subsets of a countable set with finite intersections ExampleOfUnderdeterminedPolynomialInterpolation example of under-determined polynomial interpolation ExampleOfUseOfTaylorsTheorem example of use of Taylor’s theorem ExampleOfUsingEisensteinCriterion example of using Eisenstein criterion ExampleOfUsingLagrangeMultipliers example of using Lagrange multipliers ExampleOfUsingResidueTheorem

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。

convergence of a sequence with finite upcrossings

Theorem.