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

On 10/22/2024 12:12 PM, WM wrote:

On 22.10.2024 18:03, Jim Burns wrote:

ℕ is defined such that
n ∈ ℕ  ⇔  ∃{0,1,...,n-1,n}

>
Most of all
it is an invariable set
with all its elements existing
and subject to doubling.

...and its double is in ℕ
n ∈ ℕ  ⇔
∃{0,1,...,n-1,n}  ⇔
∃{0,1,...,n-1,n,n+1,...,n+n-1,n+n} ⇔
n+n ∈ ℕ

∀n ∈ ℕ:  2×n ∈ ℕ

>
Not if all elements are existing
before multiplication already.

The description of each element in ℕ
requires its double to also be in ℕ
...not so different from the way in which
the description of a right triangle
requires
the square of its longest side to equal
the sum of the squares of the two other sides.