Sujet : Re: Definition of real number ℝ --infinitesimal--
De : F.Zwarts (at) *nospam* HetNet.nl (Fred. Zwarts)
Groupes : comp.theoryDate : 29. Mar 2024, 22:47:39
Autres entêtes
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
User-Agent : Mozilla Thunderbird
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
…