منابع مشابه
Infinitesimals and the Continuum
The opposed concepts of continuity and discreteness have figured prominently in the development of mathematics, and have also commanded the attention of philosophers. Continuous entities may be characterized by the fact that they can be divided indefinitely without altering their essential nature. So, for instance, the water in a bucket may be indefinitely halved and yet remain water. (For the ...
متن کاملEuler, infinitesimals and limits
This paper examines the Eulerian notion of infinitesimal or evanescent quantity and compares it with the modern notion of limit and non-standard analysis concepts. The Eulerian infinitesimal, when interpreted using the conceptual instruments available to modern mathematics, seems to be a fluid mixture of different elements, a continuous leap from a vague idea of limit to a confused notion of in...
متن کاملTeaching Calculus with Infinitesimals
Synopsis This article argues that first semester calculus courses for non-mathematics majors should be taught using infinitesimals. This applies to both high school and undergraduate calculus courses. The use of infinitesimals in calculus, though more intuitive than the approach developed in the 19 th century, has been controversial for over two millennia. However, in the 20 th century their us...
متن کاملPreferential Infinitesimals for Information Retrieval
In this paper, we propose a preference framework for information retrieval in which the user and the system administrator are enabled to express preference annotations on search keywords and document elements, respectively. Our framework is flexible and allows expressing preferences such as “A is infinitely more preferred than B,” which we capture by using hyperreal numbers. Due to the widespre...
متن کاملEnlarging the Bounds of Moral Philosophy: Why Did Isaac Newton Conclude the Opticks the Way He Did?
This paper draws attention to the remarkable closing words of Isaac Newton’s Optice (1706) and subsequent editions of the Opticks (1718, 1721), and tries to suggest why Newton chose to conclude his book with a puzzling allusion to his own unpublished conclusions about the history of religion. Newton suggests in this concluding passage that the bounds of moral philosophy will be enlarged as natu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1975
ISSN: 0315-0860
DOI: 10.1016/0315-0860(75)90137-8