Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logicDate : 10. Nov 2024, 11:54:02
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vgq3ca$beif$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
User-Agent : Mozilla Thunderbird
On 10.11.2024 11:20, Mikko wrote:
On 2024-11-09 21:30:47 +0000, WM said:
On 09.11.2024 15:03, Mikko wrote:
On 2024-11-08 16:30:23 +0000, WM said:
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If Cantors enumeration of the rationals is complete, then all rationals
are in the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1, ... and none is outside.
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All positive rationals quite obviously are in the sequence. Non-positive
rationals are not.
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Therefore also irrational numbers cannot be there.
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That is equally obvious.
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Of course this is wrong.
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You may call it wrong but that's the way they are.
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The measure of all intervals J(n) = [n - √2/10, n + √2/10] is smaller than 3.
Maybe, maybe not, depending on what is all n.
It is, as usual, all natural numbers.
If all n is all reals then
the measure of their union is infinite.
But n is all reals as you could have found out yourself, by the measure < 3.
Regards, WM
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