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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sat, 19 Oct 2024 07:11:19 -0400
Organization: Peripheral Visions
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Jim Burns pretended :
> 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.

Fighting fire with fire. :)

> 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.

No matter how much one wishes it did.