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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: how
Date: Sat, 20 Apr 2024 09:07:47 -0400
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On 4/19/24 11:20 AM, WM wrote:
> Le 19/04/2024 à 00:35, Richard Damon a écrit :
>> On 4/18/24 11:05 AM, WM wrote:
>>> ω is amidst the interval (0, ω2) because in the image there are as 
>>> many ordinals in (ω, ω2) as in (0, ω).
>>
>> But all those ordinals are transfinite ordinals, and none are the 
>> value of double a finite Natural Number.
> 
> You are in error. Counting goes like this: 1, 2, 3, ..., ω, ω+1, ω+2, .. 
> You simply pass ω although no known natural number k+1 will reach ω. But 
> by multiplication, which goes faster, you cannot pass ω?
> 
> Regards, WM

Nope.

Counting, BY DEFINITION, stays in the set of "Counting Numbers", 
otherwise know as the Ordinals (and that is the BASE Ordinals, the 
FINITE Ordinals, not the Transfinite Ordinals which require moving from 
"Counting" to Counting Infinities.)


That you think you can reach omega, the first transfinite ordinal, by 
finite counting, shows your error.

It isn't that there isn't a KNOWN Natural Number that reaches it, there 
is NO Natural Number that is before it, as there is no "last" Natural 
Number, because they are unbounded.

Your mind just can't comprehend what infinity is, and thus tries to 
comprehend it by making it something smaller than it actually is.

The set of Natural Number is Closed under Addition, Multiplication, and 
exponentiation.

After all, all Multiplication is, is a repeated addition, Multiplication 
by a Natural Number can't get you to a Number you couldn't get by addition.

n*2 = n + n, so a natural number
n*3 = n + n + n = n*2 + n, so a natural number

n*m (m > 0) = n*(m-1) + n, so a natural number by induction.

You logic, like your brain, is just exploded with inconsistancies 
because you have used it beyond its capabilities.