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On 30.10.2024 17:52, Jim Burns wrote:On 10/30/2024 11:27 AM, WM wrote:
∃⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩>If infinity is complete,n ∈ [0,ω) ⇒
the we can double all natural numbers
with the result
(0, ω)*2 = (0, ω*2).
∃⟨0,1,...,n-1,n⟩ ⇒
∃⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩ ⇒
n+n ∈ [0,ω)
>
n+n ∈ [0,ω) ⇒
∃⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩ ⇒
∃⟨0,1,...,n-1,n⟩ ⇒
n ∈ [0,ω)
>Then some products are in the interval (ω, ω*2).>
ω is infinite.
Do all numbers between 0 and ω exist such that
they can be doubled?
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