一个关于Peano公理的注记(续)

A Note on the Peano's Axioms(Continued)

证明了关于自然数集={1,2,3,…}的Peano公理系统中的第五条公理(即数学归纳原理)乃该系统中其余公理的逻辑推论.因之,可将它自该系统中删去而仅把它作为一个重要定理以优化该系统.

The writer points out the nonindependence of the Peano＇s axiom system for the natural numbers. In fact, the writer proves that the 5th axiom in that system, viz, the principle of mathematical induction, is really the logical consequence of the rest in that system.