What Makes a Theory of Infinitesimals Useful? A View by Klein and Fraenkel

نویسندگان

  • Vladimir Kanovei
  • Karin Katz
  • Mikhail Katz
  • Thomas Mormann
  • V. Kanovei
  • Karin U. Katz
  • Mikhail G. Katz
چکیده

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson’s framework therein.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Motivational and Emotional Bases of Envy

Envy is a painful and unpleasant emotion that leading to a feeling of humiliation, violence, and acrimony of the features of any person who has others. Envy is one of the emotions that can be seen in most cultures. Recognizing the importance of envy is because of violence that leads to aggressive behavior. Hostile nature of jealousy seen in many public crimes and also it can be seen in the c...

متن کامل

Comparison of Point of View based on Gérard Genette’s Focalization theory in Sophocles’ Ajax and Faulkner’s The Sound and the Fury

Sophocles’ Ajax is among the most significant plays in ancient Greek literature, and William Faulkner’s The Sound and the Fury is an important modern novel. This study considers these two works using Gérard Genette’s Focalization term in Narratology theory. Focalization is a feature of the point of view in narrative and is described by characters’ action, emotional reaction and speech. This stu...

متن کامل

Reflections on Jennifer Saul's View of Successful Communication and Conversational Implicature

Saul (2002) criticizes a view on the relationship between speaker meaning and conversational implicatures according to which speaker meaning is exhaustively comprised of what is said and what is implicated. In the course of making her points, she develops a couple of new notions which she calls “utterer-implicature” and “audience-implicature”. She then makes certain claims about the relationshi...

متن کامل

بررسی تکوین نظریۀ ولایت عارفانه بر مبنای استحالۀ تمثیلی و چگونگی انتقالِ آن به عصر سهروردی

Many researchers have researched the source of Islamic Sufism from a certain intellectual disposition. The prevailing view of these research works, is based on arbolic thinking and having centralized roots. According to the theory of allegorical Metamorphosis, each of the topics discussed in Islamic Sufism, can have separate roots. The present paper aims to show that Iranian Culture is one...

متن کامل

Comments on Edward Nelson’s “internal Set Theory: a New Approach to Nonstandard Analysis”

Do infinitesimals exist? This question arises naturally in calculus when one wants to write f(x+Δx) f(x) + f ′(x)Δx. This equation should hold for infinitesimal Δx where the notation a b means that a− b is infinitesimal. Much calculus can be done without bothering to define infinitesimal and using the equation above as a working definition of f ′(x). For mathematicians, of course, this is not a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2018