Sujet : Re: Replacement of Cardinality
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logic sci.mathDate : 04. Aug 2024, 21:23:50
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <7c5642f17367607b15d056059cce265ace05e13e@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 8/4/24 11:23 AM, WM wrote:
Le 03/08/2024 à 17:56, Richard Damon a écrit :
On 8/3/24 10:30 AM, WM wrote:
But there is not even an eps that separates half of all unit fractions.
>
Because such a question is meaningles, as there isn't a finite number that is half of the count of unit fractions.
If there are all, then there is half of all.
Regards, WM
But half of aleph_0 is just aleph_0, so doesn't actually get smaller.
That is how the logic of infinite sets works.
The "even" numbers are in once sense 1/2 the size of the Natural Numbers by dropping all the odds, but are also the same size by doubling each Natural Number.
Yes, that seems counter-intuitive, but that is just the math of infinite numbers.
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