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Le 25/08/2024 à 12:21, Jim Burns a écrit :On 8/24/2024 10:11 AM, WM wrote:
On 8/24/2024 10:11 AM, WM wrote:Le 24/08/2024 à 00:04, Jim Burns a écrit :
( Upper.boundⁿᵒᵗᐧᵂᴹ ≥ᵉᵃᶜʰ what.is.bounded.>>ω is an upper.bound of ℕᵈᵉᶠ.>
Of all upper.bounds of ℕᵈᵉᶠ, the lowest is ω.
Yes.
That's a definition of ω
>Nevertheless>
almost all natural numbers are bewteen ℕᵈᵉᶠ and ω.
Something between ℕᵈᵉᶠ and ω is
a lower.than.lowest upper.bound of ℕᵈᵉᶠ
No.
Dark numbers are not any bounds.
Bounds are definable.
Ordered largest.first, yes.Something between ℕᵈᵉᶠ and ω>
does not exist.
So the blind man argues.
>Each non.empty set of ordinals holds a first.>
Like each set of unit fractions.
Darkᵂᴹ numbers are between ω and ℕᵈᵉᶠDark numbers cannot be stepped to.>Do the natnumbers reach till omega?>ω, an upper.bound of ℕᵈᵉᶠ, is not.in ℕᵈᵉᶠ.>
The natnumbers do not reach ω
ω - 1 is the greates natural number.
if
ω-1 and each j before ω-1 can be stepped.uo.to,
then
ω and each j before ω can be stepped.up.to.
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