Re: Definition of real number ℝ --infinitesimal--

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Sujet : Re: Definition of real number ℝ --infinitesimal--
De : agisaak (at) *nospam* gm.invalid (André G. Isaak)
Groupes : comp.theory
Date : 04. Apr 2024, 20:08:12
Autres entêtes
Organisation : Christians and Atheists United Against Creeping Agnosticism
Message-ID : <uumqac$q2le$1@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 2024-04-04 08:55, olcott wrote:

Different enough to not me equal.
[0.0, 1.0] - [0.0, 1.0) = 0.0...1
0.000...2 - 0.000...1 = 0.000...1
*A good notational convention for infinitesimals*
And that's supposed to mean what exactly? That you take an unending sequence of zeros and once that unending sequence ends you tack on a 1?

0.999... + 0.000...1 = 1.0
0.999... + 0.000...2 = 1.000...1
0.999... + 0.000...3 = 1.000...2
0.999... + 0.000...n = 1.000...n-1
So what's 0.999... + 0.000...05 ? Is that half an infinitesimal shy of 1?
André
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