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

On 10/19/2024 7:10 AM, WM wrote:

On 19.10.2024 12:56, Jim Burns wrote:

A number immediately before an infinite ordinal
is an infinite ordinal.

>
That is the traditional opinion.

You do not understand what "A number..." says
because
you think 'infinite' means
'even a little beyond usable numbers',
something which it does not mean.
https://www.youtube.com/watch?v=aE9oOHrRMJI
⎛ You keep using that word.
⎝ I do not think it means what you think it means.
For finite ordinal k
each ordinal j in ⦅0,k⟧ is predecessored,
that is, j-1 exists
For infinite ordinal ξ, not that:
some ordinal β in ⦅0,ξ⟧ is un.predecessored,
that is, β-1 doesn't exist
If infinite ξ is predecessored
and some β in ⦅0,ξ⟧ is un.predecessored,
then
some ordinal in ⦅0,ξ⟧\{ξ} is un.predecessored.
But ⦅0,ξ⟧\{ξ} = ⦅0,ξ-1⟧
and
some ordinal in ⦅0,ξ-1⟧ being un.predecessored
means
ξ-1 is infinite.

It has lead to internal contradictions (vanishing Bob).

The contradictions are with
_what you think_ 'infinite' means.
(op. cit. Inigo Montoya)