transitivity

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传递性是一个数学和逻辑学概念,指如果A与B有某种关系,B与C也有这种关系,则A与C必然有这种关系。

用法要点

学术语境使用

transitivity主要用于数学、逻辑学、语言学等学术领域,描述关系的传递特性,在日常口语中较少使用。

• transitivity in mathematics
• transitivity of equality
• transitivity in logic

介词搭配

常与介词of连用,表示某种关系的传递性;也可与in搭配,表示在特定领域中的传递性。

• transitivity of the relation
• transitivity in set theory
• transitivity of preferences

句型结构

通常作为主语或宾语出现在学术讨论中,常与prove、demonstrate、establish等动词搭配。

• prove the transitivity
• demonstrate transitivity
• establish transitivity

基础例句

In our math class, we learned about the transitivity of equality: if A=B and B=C, then A=C.

在数学课上,我们学习了等式的传递性:如果A等于B,B等于C,那么A等于C。

The concept of transitivity helps us understand logical relationships more clearly.

传递性的概念帮助我们更清晰地理解逻辑关系。

When discussing preferences, economists often consider the transitivity of choices.

讨论偏好时,经济学家经常考虑选择的传递性。

高级例句

In formal logic, the transitivity of implication is a fundamental property that must be verified in proof systems.

在形式逻辑中,蕴含关系的传递性是证明系统中必须验证的基本性质。

The research paper examines the transitivity of social networks and its impact on information diffusion.

这篇研究论文探讨了社交网络的传递性及其对信息传播的影响。

In database design, ensuring transitivity in functional dependencies is crucial for maintaining data integrity.

在数据库设计中,确保函数依赖的传递性对于维护数据完整性至关重要。

高频搭配

verb

provedemonstrateestablishverifycheck

adjective

mathematicallogicalformalstrictcomplete

noun

propertyrelationprincipleconditionaxiom

adverb

mathematicallylogicallyformallystrictly

preposition

ofinfor

phrase

transitivity of equalitytransitivity in logictransitivity propertylaw of transitivity

常见错误

❌ 错误:The transitivity for the relation is important.
✓ 正确:The transitivity of the relation is important.

transitivity表示某种关系的特性时,应该用介词of而不是for,of表示所属关系。

❌ 错误:We need to consider about the transitivity.
✓ 正确:We need to consider the transitivity.

consider是及物动词,直接接宾语,不需要加介词about,这是中文思维导致的错误。

近义词辨析

transitive

transitive是形容词,描述具有传递性质的关系或动词;transitivity是名词,指传递性这一抽象概念。

A transitive relation exhibits transitivity. (一个传递关系展现出传递性。)

transferability

transferability强调可转移、可传递的实用性能力;transitivity是数学逻辑概念,指关系的必然传递特性。

The transferability of skills is important for career development, unlike the mathematical transitivity of relations. (技能的转移性对职业发展很重要,这与关系的数学传递性不同。)