Re: how

On 4/26/24 5:48 PM, Tom Bola wrote:

Chris M. Thomasson schrieb:

On 4/25/2024 1:06 PM, WM wrote:

Le 24/04/2024 à 22:07, "Chris M. Thomasson" a écrit :

On 4/24/2024 10:16 AM, WM wrote:

Le 24/04/2024 à 04:01, Richard Damon a écrit :

On 4/23/24 3:34 PM, WM wrote:

Le 23/04/2024 à 01:01, Richard Damon a écrit :

On 4/22/24 10:15 AM, WM wrote:

>

The results cannot be compressed to the interval (0, ω) of the
set { 1, 2, 3, ...}. This shows that new numbers are generated by
multiplication.
>

Of course they can be compressed into the interval (0, ω), as
every finite number n < ω, when doubled results in a finite number
2n which is also < ω.

>
Try to map the closed interval [0, ω]*2 = [0, ω*2].
If [0, ω) --> [0, ω) and ω*2 --> ω*2, then ω*2 is the only image
point in (ω, ω*2]. Infinitely many points remain empty. Crippled
mathematics. Ugly. Inacceptable.

>

Why?

>
Continuity.

>
[0, ω]*2 = { [0, w), ω } *2 = {[0, w), ω*2} since the Natural
numbers (what [0, ω) represents) are closed under multiplication.

>
Impossible if (0, ω) is completely filled. Every 2n is larger than n.

[...]
>
How can it be 100% completely filled when its unbounded?

>
Ask Cantor or Bolzano. It can also be completely counted - according to
Cantor.

>
How can you completely count an infinite unbounded set? You have some
issues WM... Deal with it. Your folly is not our problem... ;^o

 WM takes himself to be a "finitist" - he denies that there is somewhere
in the universe any infinity "realized" (judging that math is happening
in the mental space), so he combats this idea and exacts "the existence"
of a first real number right to zero and a last finite number left to w
altogether with any idea of inifinite objects elsewhere in the universe.
 

But then he wants to talk about the transfinite numbers, which just can not exist in the finite domain he tries to live in.
He seems to accept that mathematics does generate "infinite" numbers, but then wants them to still act like the finite numbers he understands, and complains about how they seem to break all the rules, so everything needs to be come "dark" to hide the problems.