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tech / sci.math / Re: Another kind of equation based on the infinitesimal difference

Re: Another kind of equation based on the infinitesimal difference

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https://www.novabbs.com/tech/article-flat.php?id=67007&group=sci.math#67007

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Date: Sat, 17 Jul 2021 12:11:11 -0700 (PDT)
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Subject: Re: Another kind of equation based on the infinitesimal difference
From: ross.fin...@gmail.com (Ross A. Finlayson)
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by: Ross A. Finlayson - Sat, 17 Jul 2021 19:11 UTC

On Saturday, July 17, 2021 at 11:41:54 AM UTC-7, mitchr...@gmail.com wrote:
> Calculus said zero and the infinitely small share a sameness.
> They are like each other. .999 repeating and one share
> first quantity difference that behave like zero instead...
>
> Mitchell Raemsch

Nilpotent or nilsquare are "these infinitesimals are so small,
even multiplied together they are zero in area".

This is where any area in terms of a line or square is large -
that that point of infinitesimals is two things a) the smoothness
of the graininess and b) the meter.

I.e. in calculus and real analysis, dxdy is a differential region,
x/oo y/oo is zero. They're both infinitesimals.

The raw differential is usually exactly the same with the
definition of "constant infinitesimal". (In the sense that
finite and non-zero differences are not infinitesimal.)

I.e. many peoples' idea from calculus is about that the
differential is not nilpotent nor nilsquare, instead that
they are exactly the differentials (or, "about the differential")
preserve scale as in meter (the scalar).

Here "exact" is pretty usual in terms.

Subject	Author
Re: Another kind of equation based on the infinitesimal difference	Ross A. Finlayson