Likewise, Infinitesimal is a concept; its value is smaller than any value you can imagine. Check out this video and you will appreciate why Infinity and Infinitesimal cannot be "explained" to someone seeking to find "applications" / "methodology".

In non-standard analysis, a monad (also called halo) is the set of points infinitesimally close to a given point.

Dec 31, 2014 · $0$ is infinitesimal. Natural language is a bad reference for mathematical definitions; it's 'optimized' for quickly conveying meaning in 'natural' settings, not for expressing things precisely.

Mar 10, 2021 · Our prof gave us the definition of the Lie group infinitesimal generator and it's kth-coordinate, he also explained why the kth-coordinate is called "the kth-coordinate", but nonetheless he didn't want to explain the Lie group infinitesimal generator because "we will understand it later as the course will continue".

Aug 3, 2017 · While it is possible to create number systems with infinitesimals, that does not validate the intuition that you've stated, that somehow $0.\overline{9}$ and $1$ differ by an infinitesimal. You lose a lot of nice properties of the real numbers when you add infinitesimals.

Jan 7, 2016 · Cauchy said that a sequence converging to zero becomes an infinitesimal rather than is an infinitesimal. The idea that he meant a null sequence to generate an infinitesimal is confirmed by the fact that he was interested in rates of growth of …

Apr 24, 2017 · and define an infinitesimal number as the difference between a convergent geometric series and its sum: $ x+1 -\displaystyle\sum_{i=0}^{n\rightarrow\infty} \left(\frac{x}{x+1}\right)^i$ If the x is the same in both the infinity and the infinitesimal their product will converge to the finite number x(x+1) as n increases without bound.

Jan 5, 2019 · That means that there is no need for the derivative, or the infinitesimal change in the vector, to be collinear -- or indeed depend in any way! -- with the vector value itself: they describe completely different things. In the case of a point moving as a function of time, they describe the position (the vector itself) and its velocity (the ...

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Aug 17, 2016 · Hence, zero is also an infinitesimal. But not necessarily exactly like other infinitesimals, because it seems you cannot add zero to itself any number of times and arrive to anything other than zero, while you can add other infinitesimals to themselves and …