Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : mikko.levanto (at) *nospam* iki.fi (Mikko)
Groupes : sci.logicDate : 21. Nov 2024, 11:59:04
Autres entêtes
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Message-ID : <vhn3po$jvo1$1@dont-email.me>
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On 2024-11-21 10:21:40 +0000, WM said:
On 21.11.2024 10:16, Mikko wrote:
On 2024-11-20 11:42:15 +0000, WM said:
The intervals before and after shifting are not different. Only their positions are.
The intervals are different. A shifted interval contains a different
set of numbers.
Consider this simplified argument. Let every unit interval after a natural number n which is divisible by 10 be coloured black: (10n, 10n+1]. All others are white. Is it possible to shift the black intervals so that the whole real axis becomes black?
Yes. Shift the interval (10n, 10n+1) to (n/2, n/2+1).
-- Mikko
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