Form Invariant High Order Differentials

Authors: Han Xiao

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.

Comments: 19 Pages.

Download: PDF

Submission history

[v1] 2019-06-26 01:58:32

Unique-IP document downloads: 18 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus