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

Liste des GroupesRevenir à c theory 
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>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
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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Date Sujet#  Auteur
28 Mar 24 * Definition of real number ℝ167wij
28 Mar 24 `* Re: Definition of real number ℝ166Fred. Zwarts
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28 Mar 24  i `* Re: Definition of real number ℝ2wij
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28 Mar 24   `* Re: Definition of real number ℝ --infinitesimal--160olcott
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28 Mar 24    i`* Re: Definition of real number ℝ --infinitesimal--6olcott
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28 Mar 24    i `* Re: Definition of real number ℝ --infinitesimal--3Andy Walker
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29 Mar 24       i    `* Re: Definition of real number ℝ --infinitesimal--132Fred. Zwarts
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