在 英语 中使用 Theorems 的示例及其翻译为 中文
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The log sum inequality is an inequality, which is useful for proving several theorems in information theory.
对数求和不等式（Logsuminequality）是一个不等式，可用于证明信息论中的多个定理。This means that there is a computer program that, in principle, could enumerate all the theorems of the system without listing any statements that are not theorems. .
这意味着，在原则上计算机程序能够列举出系统中所有的定理，而不列出任何非定理的陈述。Economics is not only not derived from experience, it is even impossible to verify its theorems by appeal to experience.
Reacher and Dixon had spent the occasional hour trying to prove or disprove various famous mathematical theorems.
达到和迪克森花了偶尔的小时试图证明或驳斥各种著名的数学定理。Furthermore, observe that Heyting algebras are not self dual, and thus using filters in place of ideals yields different theorems in this setting.
进一步的，观察到Heyting代数不是自对偶的，因此使用滤子替代理想在这种设置下产生不同的定理。This is perfectly natural: mathematics has an internal organic structure, deriving new theorems from those that have come before.
这是很自然的：数学有其内在的组织结构，它总是从以已有的结论导出新的定理。As a student progresses through the major, students learn how to do complex calculations and the theorems behind these calculations.
当学生通过专业进步，学生学习如何做复杂的计算和这些计算背后的定理。The differences between Schumpeter and Keynes go much deeper than economic theorems or political views.
The particular system presented here has no initial points, which means that its interpretation for logical applications derives its theorems from an empty axiom set.
这里表述的特定系统没有起始点，这意味着它对逻辑应用的解释是从空公理集合中推导出其定理的。Based on this assumption, they developed some theorems to outline the relation between a simulating and a simulated system, offering several examples for each one.
基于这一假设，他们发展了一些定理来概括模拟系统和模拟系统之间的关系，为每一个定理提供了几个例子。As in natural deduction, theorems are those B{\displaystyle B} where⊢ B{\displaystyle\vdash B} is the conclusion of a valid proof.
如同自然演绎，定理是那些B{\displaystyleB}这里的⊢B{\displaystyle\vdashB}是有效证明的结论。Historically, the first statement relating to later prime ideal theorems was in fact referring to filters- subsets that are ideals with respect to the dual order.
历史上，与后来的素理想定理有关的第一个陈述实际上提及的是滤子--它是关于对偶次序的理想的子集。In contrast, strong prime ideal theorems require that every ideal that is disjoint from a given filter can be extended to a prime ideal that is still disjoint from that filter.
相反的，“强素理想定理”要求不相交于给定滤子的所有理想可以扩展成仍不相交于这个滤子的素理想。The Nash embedding theorems(or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space.
納許嵌入定理(Nashembeddingtheorems)：，以约翰·福布斯·纳什命名，指出每个黎曼流形可以等距嵌入到欧几里得空间Rn。Many forms of these theorems are actually known to be equivalent, so that the assertion that"PIT" holds is usually taken as the assertion that the corresponding statement for Boolean algebras(BPI) is valid.
很多形式的这种定理实际上已知是等价的，所以“PIT”成立的断言通常被接受为相应的布尔代数陈述（BPI）是有效的断言。It starts with fundamental physics, circuit elements, linear and nonlinear circuits, nodal and mesh analysis, network theorems, time-domain analysis of circuits and systems.
它始于基础物理学，电路元件，线性和非线性电路，节点和网格分析，网络定理，电路和系统的时域分析。Mathematicians were not immune, and at a mathematics conference in July, 1999, Paul and Jack Abad presented their list of"The Hundred Greatest Theorems.
数学家并没有免疫这些影响，在1999年7月的一个数学会议中，Paul和JackAbad提出了他们的“一百个最伟大的定理”名单。Definitions went on for pages, followed by theorems whose statements were similarly long, but whose proofs only said, essentially,“this follows immediately from the definitions.”.
定义展开了好几页，接着是陈述同样长的定理，但是这些定理的证明本质上却只是说“根据定义可以立即得到”。Then, we will take a step back and study contingent claims and the theorems showing the existence of a discount factor(the m in p=E(mx)).
然后，我们将退一步学习或有索取权和证明折现因子（p=E(mx)中的m）存在的定理。For any class C of Kripke frames, Thm(C) is a normal modal logic(in particular, theorems of the minimal normal modal logic, K, are valid in every Kripke model).
对于Kripke框架的任何类C，Thm(C)是正规模态逻辑；特别是，最小化正规模态逻辑K的定理，在所有Kripke模型中都是有效的。
