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

On 10/19/2024 4:28 AM, WM wrote:

On 18.10.2024 14:26, Jim Burns wrote:

There is no ω
such that the numbers are
evenly.spaced between 0 and ω
because
that describes a finite ordinal, not ω

>
What is immediately before ω
if not finite numbers?

🛇⎛ And what about equilateral right triangles?
🛇⎝ Explain them, too!
A number immediately before an infinite ordinal
is an infinite ordinal.
For finite ordinal k,
k and each prior j < k
has an immediate predecessor
  or is 0
There is a general rule not open to further discussion:
An infinite ordinal is not finite.
For infinite ordinal ξ,
ξ or one of prior β < ξ
doesn't have an immediate predecessor
  and isn't 0
For infinite ordinal ξ having ξ-1,
ξ or ξ-1 or one of prior β < ξ-1
doesn't have an immediate predecessor
  and isn't 0
But ξ has an immediate predecessor.
The predecessor.free isn't ξ
For infinite ordinal ξ having ξ-1,
ξ-1 or one of prior y < ξ-1
doesn't have an immediate predecessor
  and isn't 0
For infinite ordinal ξ having ξ-1,
ξ-1 is infinite.

What is immediately before ω
if not finite numbers?

No number exists immediately before ω
ω-1 can't be infinite and must be infinite.
ω-1 can't exist.