Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of rea...Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of real numbers is of measure zero. The proposition just mentioned is basically consistent with Poincare's famous remark which renders a deep insight into the paradoxical structural nature of Cantor's continuum consisting precisely of all distinct real numbers.展开更多
This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC）...This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC） was given previously^[3]. Here we construct a new hyperstandard model [PC] instead of （PC）, and present three propositions related to the concept of semi-infinitesimal. Finally, an application of R （non-Cantorian continuum） in Calculus is expounded.Keywords Poincar6＇s intimate bond （IB）; hyperstandard microinterval; semi-infinitesimal; non-punctiform element.展开更多
基金Supperted by Special Foundation of Dalian Univ. of Technology.
文摘Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of real numbers is of measure zero. The proposition just mentioned is basically consistent with Poincare's famous remark which renders a deep insight into the paradoxical structural nature of Cantor's continuum consisting precisely of all distinct real numbers.
文摘This is an expositive paper reflecting certain viewpoint of intuitionists for the structure of continuum. What we provide is a descriptive theory for Poincaré-type continuum whose first hyperstandard model （PC） was given previously^[3]. Here we construct a new hyperstandard model [PC] instead of （PC）, and present three propositions related to the concept of semi-infinitesimal. Finally, an application of R （non-Cantorian continuum） in Calculus is expounded.Keywords Poincar6＇s intimate bond （IB）; hyperstandard microinterval; semi-infinitesimal; non-punctiform element.
