# Questions tagged [infinitesimals]

For questions about infinitesimals, both in an intuitive sense as well as more rigorous settings (see also [nonstandard-analysis]).

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### Use of elemental length in volume of a truncated cone

The typical way to compute the volume of a truncated cone is to slice into discs and calculate the volume of a differential cylinder. While doing that we first take the area of the disc $\pi f(x)^2$ ...
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### How to prove that hypotenuse of differential triangle coincides with the segment of the curve?

I read in one article that "for any curve given by an algebraic equation, the hypotenuse of the differential triangle generated by an infinitesimal abscissal increment $\varepsilon$ coincides ...
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### Is it possible to say that $dx$ indistinguishable from zero in classical analysis as $\varepsilon$ in Smooth Infinitesimal Analysis? [closed]

$dx$ isn't nonzero infinitesimal in classical analysis. Is it possible to say that $dx$ indistinguishable from zero in classical analysis as $\varepsilon$ in Smooth Infinitesimal Analysis? Thanks.
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### What is the reciprocal of an infinitesimal?

"An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity." (https://mathworld.wolfram.com/Infinitesimal.html) What is the ...
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### Proving a Definite-Integral Lies Between Two Values

I'm trying to solve the following inequation but not sure what I'm supposed to do, I know it's an integral of an even function over a symmetric interval, so I can double the area over the positive x-...
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### Clarification on Nonstandard Analysis: Is $0.\overline{9}=1$, is it not, or is there some subtlety that allows both interpretations?

This, I hope, is not a duplicate; I am exercising my critical thinking here and I want to understand what going on, and the available content I have found online on this so far has not helped. I'm ...
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### Intuition behind Lie algebra being an "infinitesimal transformation"

I have been having some trouble intuitively understanding the "infinitesimal" behavior of a Lie algebra. Currently, I think of Lie groups intuitively being a group of continuous ...
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### Infinitesimals of a higher order and limit

I read in Bartholomew Price book ("A treatise of infinitesimal calculus") that "the last term of which equality must be neglected, because it contains infinitesimals of a higher order ...
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### Algebraic property of infinitesimals $(m+dx=m)$

If $m$ is real number and $dx$ is infinitesimal, then $m+dx=m$ (if $dx$ is infinitesimal and $dx^2$ is infinitesimal, then $dx+dx^2=dx$). I suppose that $m+dx=m$, because if $\dfrac{m}{dx}=N$ ($N$-...
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