非标准分析与导数的本质

On the innate character of derivation and nonstandard analysis

采用Cauchy序列等价类来界定实数的办法,设法用某种实数序列的等价类来构造超实数域。如同在标准平面上建立标准直角坐标系那样在非标准平面上建立非标准直角坐标系,并且我们用非标准分析中的观点辩证地阐述了导数和微分的本质,以及点的可分性、曲和直的辩证统一性。

In this article,consulting the method of using Cauchy Sequence Lcassification to define real number,we use the equivalent category of real number sequence to construct su-per real,unmber field.In this way,referring to the standard plane to establish the standard right-angled coordinate system.We can construct the unstandard right-analed coordinate sys-tem in the unstandard plane,we set forth the property of differentiation in the way of nonstan-dard analysis,and the dialectical unity of differentiableness of point,curve and line.