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

On 9/24/2024 3:28 PM, WM wrote:

On 23.09.2024 19:58, Jim Burns wrote:

On 9/23/2024 8:57 AM, WM wrote:

a smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ,
is gibberish.

>
But
the increase of NUF(x) from 0 to infinity
without intermediate steps is not gibberish?

Anything which
can be reached by intermediate steps
is not infinite.
(You (WM) apparently mean something different.)
Thus
increasing NUF(x) from 0 to infinity
WITH intermediate steps
is gibberish,
in the same way in which
a right triangle without a right angle
is gibberish.
Of many suitable definitions of natural numbers,
one is:
they are well.ordered (subsets minimummed or empty)
they continue (have successors)
they are reached by a step (≠0 have predecessors)
The natural numbers are our Paradigm of Finite.
There is no first unreachable natural number.
By that and by its well.order,
there is no unreachable natural number.
ω is not a natural number.
⎛ Each before ω can be reached.
⎝ Each which can be reached is before ω.
If ω-1 existed such that (ω-1)+1 = ω
then ω could be reached
and w+1 could be reached, even though not.before ω
But that's not ω
ω-1 does not exist
in the same way in which
four.cornered.triangles do not exist.
They are gibberish,
descriptions describing nothing.