Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/20/2024 4:42 PM, WM wrote:

On 20.10.2024 22:23, Jim Burns wrote:

If n is in the set ℕ≠{1,...,n} of finites,
then 2⋅n is in the set ℕ≠{1,...,n} of finites.

>
When the elements of any set of naturals are multiplied by 2,

∃{1,2,...,n-1,n}  ⇔
∃{1,2,...,n-1,n,n+1,...,n+n-1,n+n}

their density is halved,
their reality remains the same,
their extension is doubled.
Therefore
the image contains numbers which are not in the range.

n ∈ ℕ  ⇔  ∃{1,2,...,n-1,n}
∃{1,2,...,n-1,n}  ⇔  ∃{1,2,...,n-1,n,n+1,...,n+n-1,n+1}
∃{1,2,...,n-1,n,n+1,...,n+n-1,n+1}  ⇔  n+n ∈ ℕ
n ∈ ℕ  ⇔  n+n ∈ ℕ