Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

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Sujet : Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 02. Apr 2025, 15:28:25
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vsjhia$1r7d0$7@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
User-Agent : Mozilla Thunderbird
On 28.03.2025 06:02, Moebius wrote:
Am 28.03.2025 um 02:02 schrieb Moebius:
Am 27.03.2025 um 21:11 schrieb WM:
Am 26.03.2025 um 23:18 schrieb Moebius:
Am 26.03.2025 um 22:38 schrieb Alan Mackenzie:
WM <wolfgang.mueckenheim@tha.de> wrote:
>
>
The number of [...] rooms in Hilbert's hotel is infinite but [...] grow[s].
>
No, it doesn't.
>
And the number of guests?
>
Is still the same: aleph_0.
>
It's just the "reality" (->Cantor) of guests that has grown by one. :-)
 In other words, {g_0, g_1, g_2, g_3, ...} has more "substance" (->Moebius) than {g_1, g_2, g_3, ...}, though both sets have the same cardinality (i.e. cardinal number).
In other words, cardinality cannot distinguish between the full substances of sets because it counts only the first elements.
Regards, WM

Date Sujet#  Auteur
12 Mar 25 * The existence of dark numbers proven by the thinned out harmonic series451WM
12 Mar 25 `* Re: The existence of dark numbers proven by the thinned out harmonic series450Alan Mackenzie
12 Mar 25  `* Re: The existence of dark numbers proven by the thinned out harmonic series449WM
12 Mar 25   `* The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]448Alan Mackenzie
12 Mar 25    +* Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]444WM
12 Mar 25    i+* Re: The non-existence of "dark numbers"414Alan Mackenzie
12 Mar 25    ii`* Re: The non-existence of "dark numbers"413WM
12 Mar 25    ii `* Re: The non-existence of "dark numbers"412Alan Mackenzie
12 Mar 25    ii  +* Re: The non-existence of "dark numbers"6Moebius
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15 Mar 25    ii  iii  i i i `* Re: The non-existence of "dark numbers"3Chris M. Thomasson
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