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数学充满了辩证法.数学教学是学生接受辩证唯物主义教育的重要途径.数列与极限部分的教学,可以使学生了解到特殊与一般,有限与无限,精确与近似的辩证关系,树立辩证唯物主义观点.然而,令人惊讶的是,一些教学出版物中存在着不容忽视的误区,因而也不可避免地反映在教学活动中.1 误区一览下面是从两本流行很广的教学出版物的摘录:1)“数列1,2,3,…,就是数列{n}.”2)“数列-1,1,-1,1,…,是有界数列.”3)“已知数列3,3,15,…,则9是这个数列的第项.”4)“试求数列27,411,12,45,…,的通项公式.”5)“数列12×5,15×8,18×11,…,前n项的和为.”6)“… 相似文献
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证明了{n(16n^2+4n+3)/16n^2-4~n+3^(1/2) integral from 0 to π/2 sin^nxdx}为严格单调增加数列,且极限为π/2^(1/2),因而得π(16n^2+36n+23)/2(n+1)(16n^2+28n+15)^(1/2)相似文献
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We obtain sufficient conditions excluding the existence of nontrivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of isometries and are supported on the limit set in a strong sense. 相似文献
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本文建立了有限变形的极限分析的变分原理(定理1),证明了它与有限变形的极限分析的全套方程和条件等价.本文又证明了:根据此变分原理求得的有限变形的极限载荷乘子,介于有限变形的极限分析的上限定理和下限定理所分别给出的上限解和下限解之间. 相似文献
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A set function is a function whose domain is the power set of a set, which is assumed to be finite in this paper. We treat a possibly nonadditive set function, i.e., a set function which does not satisfy necessarily additivity, ?(A) + ?(B) = ?(A ∪ B) forA ∩ B = ∅, as an element of the linear space on the power set. Then some of the famous classes of set functions are polyhedral in that linear space, i.e., expressed by a finite number of linear inequalities. We specify the sets of the coefficients of the linear inequalities for some classes of set functions. Then we consider the following three problems: (a) the domain extension problem for nonadditive set functions, (b) the sandwich problem for nonadditive set functions, and (c) the representation problem of a binary relation by a nonadditive set function, i.e., the problem of nonadditive comparative probabilities. 相似文献
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通过对Cantor三分集本质结构进行深刻洞察,并结合结构化方法对Cantor三分集的定义方式进行研究.定义了?上的无再生三分族、Cantor三分族等概念,证明了Cantor三分集的一个非三进制数模式的新公式,并证明了一个关于三进制数的新公式.为Cantor三分集的"三进制数定义法"提供了一种严密的理论基础,同时也增进了... 相似文献
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