An infinitesimal is either a positive infinitesimal, a negative infinitesimal, or zero. In $\mathbb {R}$ there is only one infinitesimal, zero - this is precisely the Archimedean property of $\mathbb {R}$.

Dec 4, 2016 · Covering 1.4 of Keisler's Elementary Calculus, "Slope and Velocity; The Hyperreal Line" That chapter defines: A number $\\epsilon$ is said to be infinitely small, infinitesimal, if: $-a < \\epsil...

Jan 7, 2016 · If you want to use infinitesimals to teach calculus, what kind of example of an infinitesimal can you give to the students? What I am asking for are specific techniques for explaining infinitesimal...

Dec 31, 2014 · For the definition of Infinitesimal, wikipedia says In common speech, an infinitesimal object is an object which is smaller than any feasible measurement, but not zero in size; or, so small t...

Dec 23, 2024 · While it might work as a separate question, I suggest coming back to it after working through one or more textbooks on Smooth Infinitesimal Analysis or Synthetic Differential Geometry. …

6 When considering an infinitesimal distance/interval/in calculus, what is the intuitive interpretation? Is it too small to be measurable but still has some distance on an unattainable scale? Are there different …

Aug 3, 2017 · There is an $\epsilon$ (infinitesimal) thrown in there as well. How do you understand these extremely small values and what do I need to do to account for them when calculating very …

Oct 31, 2025 · The term infinitesimal generator is often used in physics, where it refers to the Lie algebra elements of a Lie group. The group reflects the flows, the Lie algebra the vector field. Hence, when a …

Oct 10, 2020 · How exactly is "infinitesimal" calculus different from "limit-based" calculus? I've heard people argue over which is the "best approach" to the subject, and I've read numerous books and …

Sep 5, 2020 · The biggest problem with the concept of an infinitesimal in my mind is that they suggest that there is a 'smallest possible number'. Actually, when we are working with the standard real …