Re: Does the number of nines increase?

Liste des GroupesRevenir à s math 
Sujet : Re: Does the number of nines increase?
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.math
Date : 09. Jul 2024, 23:59:57
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v6kfdd$1if52$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
User-Agent : Mozilla Thunderbird
Am 09.07.2024 um 23:34 schrieb Chris M. Thomasson:
On 7/9/2024 2:07 PM, Moebius wrote:
Am 09.07.2024 um 22:10 schrieb Chris M. Thomasson:
On 7/9/2024 3:11 AM, FromTheRafters wrote:
>
Does that mean there are as many rationals as there are reals?
>
I already told you that: The set of rational numbers is countable infinite while the set of real numbers is _uncountable_.
>
Again: One of my math professors once tried to express this state of affairs the following way: "There are (in a certain sense) much more real numbers than rational numbers."
 Strange that any real can be represented by a rational up to infinite precision...
It's even worse: Between any two (different) real numbers there's a rational number and between any two (different) rational numbers there's a real number!
So how can there be "more" real numbers than rational numbers? :-P
This is one of WM's arguments to show that card(IR) and card(Q) are the same (iirc). Needless to say that it is incorrect.

Date Sujet#  Auteur
25 Jun 24 * Does the number of nines increase?427WM
26 Jun 24 +* Re: Does the number of nines increase?358Jim Burns
26 Jun 24 i`* Re: Does the number of nines increase?357WM
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26 Jun 24 i i+* Re: Does the number of nines increase?310Chris M. Thomasson
26 Jun 24 i ii`* Re: Does the number of nines increase?309Jim Burns
27 Jun 24 i ii `* Re: Does the number of nines increase?308WM
27 Jun 24 i ii  +* Re: Does the number of nines increase?84FromTheRafters
27 Jun 24 i ii  i`* Re: Does the number of nines increase?83WM
28 Jun 24 i ii  i +* Re: Does the number of nines increase?81Richard Damon
28 Jun 24 i ii  i i`* Re: Does the number of nines increase?80WM
29 Jun 24 i ii  i i +* Re: Does the number of nines increase?11Chris M. Thomasson
29 Jun 24 i ii  i i i`* Re: Does the number of nines increase?10WM
29 Jun 24 i ii  i i i +* Re: Does the number of nines increase?3Chris M. Thomasson
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4 Jul 24 i ii  i i   `* Re: Does the number of nines increase?56Jim Burns
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