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- W2955067973 abstract "Traditionally, an infinitesimal is regarded as a variable that runs toward 0. Since a differential is a kind of infinitesimal, a differential is essentially a variable running toward 0 too. As a result, differentials are form invariant but not meaning invariant. This paper proposes a Number Field of Ordered Infinitesimals and Infinities (OII Number Field) which can be seen as a kind of extension of real number field. The terminus of a variable running toward 0 is no longer 0, but a point in the OII Number Field, with an Order and a Weight. In this way, the process of running is recorded in the destination, making infinitesimals a kind of number which can be compared and operated easily. On this basis, the differential of a variable is invariant not only in form, but also in meaning. As a differential becomes a variable on another number axis parallel to the real number axis in OII Number Field, a differential can generate differential too, thus giving rise to high order differentials which are also invariant both in form and in meaning." @default.
- W2955067973 created "2019-07-12" @default.
- W2955067973 creator A5034681839 @default.
- W2955067973 date "2019-06-01" @default.
- W2955067973 modified "2023-09-24" @default.
- W2955067973 title "Form Invariant High Order Differentials" @default.
- W2955067973 hasPublicationYear "2019" @default.
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