【英语】theorem的例句

时间: 2024-11-07 20:02:07

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1. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. (毕达哥拉斯定理表明，在直角三角形中，斜边的长度的平方等于另外两条边长的平方和。)

2. Fermat's Last Theorem, which stumped mathematicians for centuries, was finally proved by Andrew Wiles in 1994. (费马大定理曾使数学家们困惑了几个世纪，直到1994年安德鲁·怀尔斯终于证明了它。)

3. The central limit theorem is a fundamental concept in statistics, describing the behavior of the distribution of sample means. (中心极限定理是统计学中的基本概念，描述了样本均值分布的行为。)

4. Gödel's incompleteness theorem shook the foundations of mathematics by demonstrating that certain statements cannot be proven within a formal system. (哥德尔的不完备定理通过证明某些陈述在形式系统中无法证明，震撼了数学的基础。)

5. The fundamental theorem of calculus connects the concept of differentiation and integration, showing that they are inverse operations. (微积分基本定理连接了微分和积分的概念，表明它们是互为逆运算的。)

6. The Banach-Tarski paradox, based on the Axiom of Choice, is a theorem in set-theoretic geometry that states a sphere can be decomposed into a finite number of pieces and reassembled into two spheres identical to the original. (巴拿赫-塔斯基悖论基于选择公理，是集合论几何学中的一个定理，它表明一个球可以分解成有限数量的部分，然后重新组装成两个与原来相同的球。)

7. The Bolzano-Weierstrass theorem guarantees that every bounded sequence in real numbers has a convergent subsequence. (玻尔查诺-魏尔斯特拉斯定理保证了实数中的每个有界序列都有一个收敛的子序列。)

8. The theorem of the mean value, also known as the mean value theorem, states that for a continuous function on a closed interval, there exists a point where the derivative is equal to the average rate of change of the function. (平均值定理，也称为平均值定理，表明对于闭区间上的连续函数，存在一个点，该点的导数等于函数的平均变化率。)

9. The Brouwer fixed-point theorem asserts that any continuous function from a closed ball to itself must have a fixed point. (布劳威尔不动点定理断言，从闭球到自身的任何连续函数必须有一个不动点。)

10. The prime number theorem gives an asymptotic description of the distribution of prime numbers. (素数定理对素数的分布给出了渐近描述。)

11. The Hahn-Banach theorem is a fundamental result in functional analysis, providing a way to extend bounded linear functionals defined on a subspace to the entire space. (哈恩-班奈赫定理是功能分析中的一个基本结果，提供了一种将定义在子空间上的有界线性泛函扩展到整个空间的方法。)

12. The Riemann mapping theorem states that any simply connected open subset of the complex plane that is not the whole plane can be conformally mapped onto the unit disk. (黎曼映射定理表明，任何复平面上的非整个平面的单连通开子集都可以共形映射到单位圆盘上。)

13. The Jordan curve theorem states that a simple closed curve divides the plane into exactly two regions, an inside and an outside. (约当曲线定理表明，一个简单封闭曲线将平面分成两个区域，内部和外部。)

14. The Gauss-Bonnet theorem relates the curvature of a surface to its topology, providing a deep connection between geometry and topology. (高斯-邦奈特定理将曲面的曲率与其拓扑联系起来，为几何和拓扑之间提供了深刻的联系。)

15. Gödel's completeness theorem states that any consistent first-order theory has a model, or in other words, that every logically possible structure has a model in some set theory. (哥德尔的完备性定理表明，任何一致的一阶理论都有一个模型，换句话说，每个逻辑上可能的结构在某个集合论中都有一个模型。)