对自然数定义的一些注记

Some Notes on the Definition of Natural Number

利用公理化方法,通过定义非空集上的二元关系"π",使该集合构成全序集,然后在该集合中给出以含有最小元素原理或最大元素原理的适当公理体系来重新刻画自然数的定义,最后证明这些定义与自然数的皮亚诺公理定义彼此是等价的。

In this paper, we first define the binary relation in nonvoid set and make the congregation a total ordering. Then we redefine natural number by giving out proper axiom system with principle of the least element and principle of the greatest element in the set. Finally, we prove that these axioms are equivalences to natural number＇s Peano Axiom.