Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.math
Date : 14. Oct 2024, 23:27:14
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vek5s2$1c3q2$2@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
User-Agent : Mozilla Thunderbird
On 10/14/2024 9:37 AM, WM wrote:
On 14.10.2024 18:04, joes wrote:
Am Mon, 14 Oct 2024 15:40:01 +0200 schrieb WM:
On 14.10.2024 14:15, joes wrote:
>
No, we are taking the complete, actually infinite set which reaches to
"before" w.
and fills the space between 0 and ω evenly. Same happens with the
doubled set between 0 and ω2.
No, there is no consequent infinity. The even numbers do not go
0, 2, 4, ..., w, w+2, w+4, ..., w*2
 Either the doubled numbers are natural, then half of them have not been among the original set, or all natural numbers have been doubled, then the result contains infinite numbers.
 That doubling _all_ natural numbers only yields _all_ natural numbers is impossible.
Take the index, using natural numbers
1: { 1 }
2: { 1, 2 }
3: { 1, 2, 3 }
4: { 1, 2, 3, 4 }
...
vs:
1: { 2 }
2: { 2, 4 }
3: { 2, 4, 6 }
4: { 2, 4, 6, 8 }
...

Date Sujet#  Auteur
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