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Am Wed, 31 Jul 2024 14:27:06 +0000 schrieb WM:Dark natnumbers are larger than defined natnumbers. Even dar natnumbers can be compared by size. ω/10^10 < ω/10 < ω/2, < ω-1.Le 31/07/2024 à 03:28, Richard Damon a écrit :That is a bit imprecise. Even though you keep on talking aboutOn 7/30/24 1:37 PM, WM wrote:In the midst, far beyond all definable numbers, far beyond ω/10^10.Le 30/07/2024 à 03:18, Richard Damon a écrit :And where is that in {1, 2, 3, ... w} ?On 7/29/24 9:11 AM, WM wrote:ω/2But what number became ω when doubled?
consecutive infinities, you can't compare natural and "dark" numbers.
What is immediately before ω? Is it a blasphemy to ask such questions?ω/10^10 and ω/10 are dark natural numbers.Completeness of N? No number n reaches omega.
I assume completness.But you combined two different sets, so why can't there be a gap?Because otherwise there was a gap below ω.If all natural numbers exist, then ω-1 exists.Why?
It is not a contradiction to my formula if some n has no n+1.That is not a contradiction.No. My formula says ∀n ∈ ℕ.∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Note the universal quantifier.Right, so we can say that ∀n ∈ ℕ: 1/n > 1/(n+1), so that for every unit
fraction 1/n, there exists another unit fraction smaller than itself.
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