Sujet : Re: Definition of real number ℝ --infinitesimal--
De : polcott333 (at) *nospam* gmail.com (olcott)
Groupes : comp.theoryDate : 04. Apr 2024, 21:57:17
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <uun0mt$rl7d$1@dont-email.me>
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User-Agent : Mozilla Thunderbird
On 4/4/2024 1:08 PM, André G. Isaak wrote:
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?
That is 5 infinitesimals.
Do you have a better way to encode them?
André
-- Copyright 2024 Olcott "Talent hits a target no one else can hit; Geniushits a target no one else can see." Arthur Schopenhauer
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