How to calculate the order of an infinitesimal

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Discussion Overview

The discussion revolves around the concept of determining the order of infinitesimals in calculus. Participants explore how to classify infinitesimals as first, second, or higher order, and the relative nature of this classification.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant describes a method for identifying first-order infinitesimals using the relationship between delta values and derivatives.
  • Another participant asserts that the order of an infinitesimal is always relative, prompting questions about the basis for this relativity.
  • A follow-up question seeks clarification on what the order is relative to and how to determine it.

Areas of Agreement / Disagreement

Participants express differing views on the nature of infinitesimal order, with some asserting its relativity while others seek more concrete definitions and methods for classification. The discussion remains unresolved.

Contextual Notes

There are missing assumptions regarding the definitions of order and the context in which infinitesimals are being evaluated, as well as unresolved mathematical steps related to higher-order classifications.

NBagley119
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I know how to find out if an infinitesimal delta is of the first order (if delta*y/delta*x=dy/dx+epsilon is approximately equal to (dy/dx)*delta*x, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?

Note: I will update this question with typesetting once I figure out how to use LaTeX.
 
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The order of an 'infinitesimal' is always relative.
 
Eynstone said:
The order of an 'infinitesimal' is always relative.

Relative to what? And how do you find the order?
 
I know how to find out if an infinitesimal delta is of the first order (if \frac{\delta y}{\delta x}=\frac{dy}{dx}+\epsilon\approx\frac{dy}{dx}\deltax, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?
 

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