quod erat demonstrandum=which has to be proved

简明释义

证讫

英英释义

例句

1.In her dissertation, she used quod erat demonstrandum=which has to be proved to conclude her mathematical proofs.

在她的论文中，她使用quod erat demonstrandum=which has to be proved来结束她的数学证明。

2.The lawyer presented his argument and finished with quod erat demonstrandum=which has to be proved to emphasize his point.

律师提出了他的论点，并以quod erat demonstrandum=which has to be proved结束，以强调他的观点。

3.In proving the theorem, the mathematician concluded with the statement quod erat demonstrandum=which has to be proved.

在证明这个定理时，数学家以quod erat demonstrandum=which has to be proved的声明结束。

4.After deriving the formula, the physicist wrote quod erat demonstrandum=which has to be proved to signify the completion of the proof.

在推导出公式后，物理学家写下quod erat demonstrandum=which has to be proved以表示证明的完成。

5.The scientist's findings were conclusive, and he stated quod erat demonstrandum=which has to be proved at the end of his report.

科学家的发现是确凿的，他在报告的最后写道quod erat demonstrandum=which has to be proved。

作文

In the realm of mathematics and logic, there exists a phrase that resonates deeply with those who seek to establish truths: quod erat demonstrandum, which has to be proved. This Latin expression, often abbreviated as Q.E.D., serves as a powerful reminder of the rigorous nature of proof and the importance of substantiating claims with evidence. The journey of proving a statement is not merely an academic exercise; it reflects a fundamental aspect of human reasoning and the quest for knowledge.To understand the significance of quod erat demonstrandum, we must first explore the concept of proof itself. Proof is the process by which we validate a hypothesis or claim through logical reasoning and empirical evidence. In mathematics, for instance, a theorem is not accepted until it has been rigorously demonstrated through a series of logical deductions based on previously established axioms and theorems. This meticulous process ensures that the conclusions drawn are not merely opinions but are grounded in verifiable truth.The phrase quod erat demonstrandum is typically placed at the end of a mathematical proof to signify that the initial statement has been conclusively proven. It is a declaration of closure, indicating that the argument has reached its intended conclusion. This practice underscores the discipline of mathematics, where every assertion requires justification, and every claim must withstand scrutiny.However, the implications of quod erat demonstrandum extend beyond the confines of mathematics. In everyday life, we often encounter situations where we need to substantiate our beliefs or decisions. Whether in scientific research, legal arguments, or even personal relationships, the ability to provide proof is essential. For example, in science, a hypothesis is only accepted after rigorous testing and validation, echoing the principles embodied in quod erat demonstrandum. Similarly, in law, a case must be proven beyond a reasonable doubt, highlighting the necessity of evidence and logical reasoning.Moreover, the pursuit of proof encourages critical thinking and skepticism. It invites individuals to question assumptions and seek clarity in their understanding. In an age where misinformation can spread rapidly, the principles behind quod erat demonstrandum remind us of the importance of verifying claims before accepting them as truth. This critical approach fosters a culture of inquiry, where ideas are challenged and refined, ultimately leading to deeper insights and advancements in knowledge.In conclusion, the phrase quod erat demonstrandum, meaning which has to be proved, encapsulates the essence of proof in both mathematics and life. It serves as a guiding principle that emphasizes the importance of substantiating claims with evidence and logical reasoning. As we navigate through various fields of knowledge, let us embrace the spirit of quod erat demonstrandum, striving to prove our assertions and contribute to a more informed and rational world.

在数学和逻辑的领域中，有一个短语与那些寻求确立真理的人深深共鸣：quod erat demonstrandum，即“必须证明”。这个拉丁表达，通常缩写为Q.E.D.，是对证明严谨本质的有力提醒，也是用证据支持主张的重要性。证明一个陈述的过程不仅仅是学术练习；它反映了人类推理的基本方面和对知识的追求。要理解quod erat demonstrandum的重要性，我们首先必须探讨证明的概念。证明是通过逻辑推理和经验证据来验证假设或主张的过程。例如，在数学中，一个定理只有在通过一系列基于先前建立的公理和定理的逻辑推导严格证明后，才会被接受。这个细致的过程确保了得出的结论不仅仅是意见，而是基于可验证的真理。短语quod erat demonstrandum通常放在数学证明的末尾，以表明初始陈述已经被确凿证明。这是一个结束的声明，表明论证已达到预期的结论。这种做法强调了数学的纪律性，在这里，每个主张都需要理由，每个主张都必须经得起审查。然而，quod erat demonstrandum的意义超越了数学的范畴。在日常生活中，我们经常遇到需要证明我们的信念或决策的情况。无论是在科学研究、法律论证，还是个人关系中，提供证明的能力都是至关重要的。例如，在科学中，只有经过严格测试和验证，假设才会被接受，这与quod erat demonstrandum所体现的原则相呼应。同样，在法律中，案件必须超出合理怀疑地得到证明，这突显了证据和逻辑推理的必要性。此外，对证明的追求鼓励批判性思维和怀疑精神。它邀请个人质疑假设，并在理解上寻求清晰。在信息传播迅速的时代，quod erat demonstrandum背后的原则提醒我们在接受主张为真之前验证其真实性的重要性。这种批判性的方法培养了一种探究文化，在这种文化中，思想受到挑战并被完善，最终导致更深刻的见解和知识的进步。总之，短语quod erat demonstrandum，意为必须证明，概括了数学和生活中证明的本质。它作为一个指导原则，强调用证据和逻辑推理来支持主张的重要性。当我们在各种知识领域中探索时，让我们拥抱quod erat demonstrandum的精神，努力证明我们的主张，为一个更明智和理性的世界做出贡献。