Sujet : Re: Does the number of nines increase?
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 09. Jul 2024, 22:49:35
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v6kb9f$1hehi$2@dont-email.me>
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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...
What is "up to infinite precision" and "represent"?
Hint: There is NO rational number such that r = sqrt(2).
Hence for each and every rational number r there is a "non zero" difference between sqrt(2) and r.
I guess you might have a _sequence_ of rational numbers in mind, say,
(1, 1.4, 1.41, 1.414, ...).
So we might say that this SEQUENCE represents the real number sqrt(2) - in a certain sense. :-P
Actually, its limit is sqrt(2).
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