24 November 2022, 13:15 (EET), Hall 300, INRNE

• Todor D. Todorov (Emeritus in Cal Poly, San Luis Obispo)
• Title: Infinitesimals in the Field of Complex Numbers
• Abstract: We show that the field of complex numbers C contains non-zero infinitesimals. They (infinitesimals) become “visible” only under ab- solute values on C different from the usual absolute value. The talk is intended as a “mathematical entertainment”, but it can be used for a more serious discussion as well. After all, any new property observed about C should be treated as a surprise, since the concept of complex numbers is one of the most popular and beloved ones in mathematics. An additional intrigue arises from the fact that infinitesimals are of- ten an object of dislike, hate and obscurity in modern mathematics in spite of (and perhaps, exactly because of) their irreplaceable role for the creation of infinitesimal calculus by Leibniz, Newton, Euler and others.
• Key Words: Totally ordered field, real closed field, Archimedean field, non-Archimedean field, algebraically closed field, Steinitz theorem, Artin- Schreier theorem, Puiseux-Newton series, Levi-Civit ́a series, Robinson’s asymp- totic numbers, Robinson’s non-standard real numbers.
• Slides
• Notes