Re: 2N=E

On 11/1/2024 6:24 AM, WM wrote:

On 01.11.2024 05:15, Jim Burns wrote:

On 10/31/2024 4:27 PM, WM wrote:

On 31.10.2024 20:25, Jim Burns wrote:

On 10/31/2024 2:30 PM, WM wrote:

Potentially infinite means
finite but variable without bound.

>
Our sets do not change.

>
Then:
Multiplication of
all infinitely many fractions of the open interval (0,1)
results in some fractions in (1, 2).

>
No.

>
If numbers are doubled, then greater numbers are produced.

Yes.
⟨0,1,...,n-1,n⟩ < ⟨0,1,...,n-1,n,n+1,...,n+n-1,n+1⟩ < ω

That is simple mathematics. There is no doubt about it.

If all natural numbers are doubled,
then not only natural numbers are produced.

No.
⟨0,1,...,n-1,n⟩ < ⟨0,1,...,n-1,n,n+1,...,n+n-1,n+1⟩ < ω
⎛ ⟨0,...,k⟩ < ω  ⇔
⎜ ∀j ∈ ⟨0,...,k⟩\⟨0⟩:
⎝ ∃i ∈ ⟨0,...,k⟩\⟨k⟩: i+1=j
∀j ∈ ⟨0,1,...,n-1,n⟩\⟨0⟩:
∃i ∈ ⟨0,1,...,n-1,n⟩\⟨n⟩: i+1=j
⟨0,1,...,n-1,n⟩ < ω
∀j ∈ ⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩\⟨0⟩:
∃i ∈ ⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩\⟨n+n⟩: i+1=j
⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩ < ω
'Infinity' does not mean what you want it to mean.