关系与映射

Relation and Mapping

集合论是现代数学的理论基础,映射是集合论中用以建立现代数学概念和理论的基本工具和手段。集合与映射是整个中学数学的理论基础。关系是在高等代数学中才出现的概念。关系和映射两个“距离”很远,看似不相干的概念,实则有着密不可分的联系:关系是映射的推广,且均可用集合表示。

Set theory is the base of modem mathematics, while the mapping is the basic tool and method in it for setting up concepts and theories of modem mathematics. Set and mapping are the basiz theories in middle school mathematics. Relation appeas in higher algebra. They seem not relevant to each other, in fact, the relation is the development of mapping,and they are all expressed by set.