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

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Sujet : Re: Definition of real number ℝ --infinitesimal--
De : F.Zwarts (at) *nospam* HetNet.nl (Fred. Zwarts)
Groupes : comp.theory
Date : 29. Mar 2024, 22:47:39
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Organisation : A noiseless patient Spider
Message-ID : <uu79db$gdqk$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
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Op 29.mrt.2024 om 16:46 schreef olcott:
On 3/29/2024 8:13 AM, Richard Damon wrote:
On 3/28/24 11:50 PM, olcott wrote:
On 3/28/2024 10:36 PM, Keith Thompson wrote:
olcott <polcott2@gmail.com> writes:
[...]
It seems dead obvious that 0.999... is infinitesimally less than 1.0.
>
Yes, it *seems* dead obvious.  That doesn't make it true, and in fact it
isn't.
>
>
0.999... means that is never reaches 1.0.
and math simply stipulates that it does even though it does not.
>
>
0.999... isn't a "number" in the Real Number system, just an alternate representation for the number 1.
>
 That is not true. 0.999... means never reaches 1.0
Maybe for olcott's unspecified olcott numbers. For real numbers 0.999... equals 1.0. There are many proofs. See e.g.
https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

Date Sujet#  Auteur
28 Mar 24 * Definition of real number ℝ167wij
28 Mar 24 `* Re: Definition of real number ℝ166Fred. Zwarts
28 Mar 24  +* Re: Definition of real number ℝ4wij
28 Mar 24  i`* Re: Definition of real number ℝ3Fred. Zwarts
28 Mar 24  i `* Re: Definition of real number ℝ2wij
28 Mar 24  i  `- Re: Definition of real number ℝ1Fred. Zwarts
28 Mar 24  `* Re: Definition of real number ℝ161Andy Walker
28 Mar 24   `* Re: Definition of real number ℝ --infinitesimal--160olcott
28 Mar 24    +* Re: Definition of real number ℝ --infinitesimal--7Andy Walker
28 Mar 24    i`* Re: Definition of real number ℝ --infinitesimal--6olcott
28 Mar 24    i +* Re: Definition of real number ℝ --infinitesimal--2wij
29 Mar 24    i i`- Re: Definition of real number ℝ --infinitesimal--1Andy Walker
28 Mar 24    i `* Re: Definition of real number ℝ --infinitesimal--3Andy Walker
28 Mar 24    i  `* Re: Definition of real number ℝ --infinitesimal--2olcott
29 Mar 24    i   `- Re: Definition of real number ℝ --infinitesimal--1Andy Walker
29 Mar 24    `* Re: Definition of real number ℝ --infinitesimal--152Richard Damon
29 Mar 24     `* Re: Definition of real number ℝ --infinitesimal--151olcott
29 Mar 24      `* Re: Definition of real number ℝ --infinitesimal--150Richard Damon
29 Mar 24       +* Re: Definition of real number ℝ --infinitesimal--148olcott
29 Mar 24       i+- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
29 Mar 24       i`* Re: Definition of real number ℝ --infinitesimal--146Keith Thompson
29 Mar 24       i `* Re: Definition of real number ℝ --infinitesimal--145olcott
29 Mar 24       i  +* Re: Definition of real number ℝ --infinitesimal--10Keith Thompson
29 Mar 24       i  i+* Re: Definition of real number ℝ --infinitesimal--8olcott
29 Mar 24       i  ii`* Re: Definition of real number ℝ --infinitesimal--7Andy Walker
29 Mar 24       i  ii `* Re: Definition of real number ℝ --infinitesimal--6olcott
29 Mar 24       i  ii  `* Re: Definition of real number ℝ --infinitesimal--5Fred. Zwarts
29 Mar 24       i  ii   +* Re: Definition of real number ℝ --infinitesimal--3wij
29 Mar 24       i  ii   i+- Re: Definition of real number ℝ --infinitesimal--1wij
29 Mar 24       i  ii   i`- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
29 Mar 24       i  ii   `- Re: Definition of real number ℝ --infinitesimal--1olcott
29 Mar 24       i  i`- Re: Definition of real number ℝ --infinitesimal--1Fred. Zwarts
29 Mar 24       i  `* Re: Definition of real number ℝ --infinitesimal--134Richard Damon
29 Mar 24       i   `* Re: Definition of real number ℝ --infinitesimal--133olcott
29 Mar 24       i    `* Re: Definition of real number ℝ --infinitesimal--132Fred. Zwarts
29 Mar 24       i     +- Re: Definition of real number ℝ --infinitesimal--1olcott
30 Mar 24       i     `* Re: Definition of real number ℝ --infinitesimal--130Keith Thompson
30 Mar 24       i      `* Re: Definition of real number ℝ --infinitesimal--129olcott
30 Mar 24       i       +* Re: Definition of real number ℝ --infinitesimal--125Keith Thompson
30 Mar 24       i       i+* Re: Definition of real number ℝ --infinitesimal--2Keith Thompson
30 Mar 24       i       ii`- Re: Definition of real number ℝ --infinitesimal--1Ross Finlayson
30 Mar 24       i       i`* Re: Definition of real number ℝ --infinitesimal--122olcott
30 Mar 24       i       i +* Re: Definition of real number ℝ --infinitesimal--5Keith Thompson
30 Mar 24       i       i i`* Re: Definition of real number ℝ --infinitesimal--4olcott
30 Mar 24       i       i i `* Re: Definition of real number ℝ --infinitesimal--3André G. Isaak
30 Mar 24       i       i i  `* Re: Definition of real number ℝ --infinitesimal--2olcott
30 Mar 24       i       i i   `- Re: Definition of real number ℝ --infinitesimal--1Keith Thompson
30 Mar 24       i       i +* Re: Definition of real number ℝ --infinitesimal--3Fred. Zwarts
30 Mar 24       i       i i`* Re: Definition of real number ℝ --infinitesimal--2olcott
30 Mar 24       i       i i `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
30 Mar 24       i       i `* Re: Definition of real number ℝ --infinitesimal--113Fred. Zwarts
30 Mar 24       i       i  `* Re: Definition of real number ℝ --infinitesimal--112olcott
30 Mar 24       i       i   +* Re: Definition of real number ℝ --infinitesimal--7Richard Damon
30 Mar 24       i       i   i`* Re: Definition of real number ℝ --infinitesimal--6wij
30 Mar 24       i       i   i `* Re: Definition of real number ℝ --infinitesimal--5Richard Damon
30 Mar 24       i       i   i  `* Re: Definition of real number ℝ --infinitesimal--4wij
30 Mar 24       i       i   i   `* Re: Definition of real number ℝ --infinitesimal--3Richard Damon
30 Mar 24       i       i   i    `* Re: Definition of real number ℝ --infinitesimal--2wij
30 Mar 24       i       i   i     `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
30 Mar 24       i       i   +- Re: Definition of real number ℝ --infinitesimal--1Fred. Zwarts
30 Mar 24       i       i   `* Re: Definition of real number ℝ --infinitesimal--103Fred. Zwarts
30 Mar 24       i       i    `* Re: Definition of real number ℝ --infinitesimal--102olcott
30 Mar 24       i       i     `* Re: Definition of real number ℝ --infinitesimal--101Fred. Zwarts
30 Mar 24       i       i      +* Re: Definition of real number ℝ --infinitesimal--98olcott
31 Mar 24       i       i      i`* Re: Definition of real number ℝ --infinitesimal--97Fred. Zwarts
31 Mar 24       i       i      i `* Re: Definition of real number ℝ --infinitesimal--96olcott
31 Mar 24       i       i      i  +* Re: Definition of real number ℝ --infinitesimal--94Fred. Zwarts
31 Mar 24       i       i      i  i`* Re: Definition of real number ℝ --infinitesimal--93olcott
31 Mar 24       i       i      i  i +- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
1 Apr 24       i       i      i  i `* Re: Definition of real number ℝ --infinitesimal--91Fred. Zwarts
1 Apr 24       i       i      i  i  `* Re: Definition of real number ℝ --infinitesimal--90olcott
1 Apr 24       i       i      i  i   +* Re: Definition of real number ℝ --infinitesimal--88Fred. Zwarts
1 Apr 24       i       i      i  i   i`* Re: Definition of real number ℝ --infinitesimal--87olcott
1 Apr 24       i       i      i  i   i +* Re: Definition of real number ℝ --infinitesimal--57Fred. Zwarts
1 Apr 24       i       i      i  i   i i`* Re: Definition of real number ℝ --infinitesimal--56olcott
1 Apr 24       i       i      i  i   i i +* Re: Definition of real number ℝ --infinitesimal--14André G. Isaak
1 Apr 24       i       i      i  i   i i i+* Re: Definition of real number ℝ --infinitesimal--6André G. Isaak
1 Apr 24       i       i      i  i   i i ii`* Re: Definition of real number ℝ --infinitesimal--5wij
2 Apr 24       i       i      i  i   i i ii +* Re: Definition of real number ℝ --infinitesimal--3wij
2 Apr 24       i       i      i  i   i i ii i`* Re: Definition of real number ℝ --infinitesimal--2Ben Bacarisse
2 Apr 24       i       i      i  i   i i ii i `- Re: Definition of real number ℝ --infinitesimal--1wij
2 Apr 24       i       i      i  i   i i ii `- Re: Definition of real number ℝ --infinitesimal--1olcott
2 Apr 24       i       i      i  i   i i i`* Re: Definition of real number ℝ --infinitesimal--7olcott
2 Apr 24       i       i      i  i   i i i `* Re: Definition of real number ℝ --infinitesimal--6Fred. Zwarts
2 Apr 24       i       i      i  i   i i i  `* Re: Definition of real number ℝ --infinitesimal--5olcott
2 Apr 24       i       i      i  i   i i i   +* Re: Definition of real number ℝ --infinitesimal--3Fred. Zwarts
2 Apr 24       i       i      i  i   i i i   i`* Re: Definition of real number ℝ --infinitesimal--2olcott
3 Apr 24       i       i      i  i   i i i   i `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
3 Apr 24       i       i      i  i   i i i   `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
2 Apr 24       i       i      i  i   i i +- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
2 Apr 24       i       i      i  i   i i `* Re: Definition of real number ℝ --infinitesimal--40Fred. Zwarts
2 Apr 24       i       i      i  i   i i  +* Re: Definition of real number ℝ --infinitesimal--36olcott
2 Apr 24       i       i      i  i   i i  i+* Re: Definition of real number ℝ --infinitesimal--34Fred. Zwarts
2 Apr 24       i       i      i  i   i i  ii`* Re: Definition of real number ℝ --infinitesimal--33olcott
3 Apr 24       i       i      i  i   i i  ii +- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
3 Apr 24       i       i      i  i   i i  ii `* Re: Definition of real number ℝ --infinitesimal--31Fred. Zwarts
3 Apr 24       i       i      i  i   i i  ii  `* Re: Definition of real number ℝ --infinitesimal--30olcott
3 Apr 24       i       i      i  i   i i  ii   +* Re: Definition of real number ℝ --infinitesimal--28Fred. Zwarts
3 Apr 24       i       i      i  i   i i  ii   i+- Re: Definition of real number ℝ --infinitesimal--1olcott
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3 Apr 24       i       i      i  i   i i  ii   i +* Re: Definition of real number ℝ --infinitesimal--19olcott
3 Apr 24       i       i      i  i   i i  ii   i `* Re: Definition of real number ℝ --infinitesimal--6Mike Terry
4 Apr 24       i       i      i  i   i i  ii   `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
3 Apr 24       i       i      i  i   i i  i`- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
2 Apr 24       i       i      i  i   i i  `* Re: Definition of real number ℝ --infinitesimal--3Mike Terry
2 Apr 24       i       i      i  i   i +* Re: Definition of real number ℝ --infinitesimal--28Keith Thompson
2 Apr 24       i       i      i  i   i `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
2 Apr 24       i       i      i  i   `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
31 Mar 24       i       i      i  `- Re: Definition of real number ℝ --infinitesimal--1Richard Damon
30 Mar 24       i       i      `* Re: Definition of real number ℝ --infinitesimal--2olcott
30 Mar 24       i       `* Re: Definition of real number ℝ --infinitesimal--3Andy Walker
29 Mar 24       `- Re: Definition of real number ℝ --infinitesimal--1wij

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