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I've been researching infinitesimals in my spare time, and have come to an hypothesis. Is it fair to say that $\varepsilon = 0.\bar01$? In English: the infinitesimal $\varepsilon$ is equal to an infinite amount of zeros after the decimal point, followed by $1$.

This would mean that the equation $\varepsilon/2=0.\bar005$ is true by extension.

Thanks.

Parcly Taxel
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HarrisonO
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  • I doubt this makes sense. Maybe you could give a reference supporting your claim? – Yuriy S Feb 09 '18 at 12:41
  • What does that notation mean? The usual definition, in $\frac 19 = .\overline 1$ for instance, means $\frac 19 = \sum_{n=0}^{\infty} 10^{-n}$. What does your notation mean? – lulu Feb 09 '18 at 13:14
  • I think the question you should be asking is: is this notation consistent with all the properties of infinitesimals? It is a good way to indicate that $\varepsilon < r$ for all real $r$, i.e. it seems to work for the ordering properties. What about the arithmetic ones? – Sort of Damocles Feb 09 '18 at 13:27

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