Re: How many ... (Sparse, Signal, Square Cantor "SPACE")

On 11/03/2024 02:53 PM, Chris M. Thomasson wrote:

On 11/3/2024 9:09 AM, Ross Finlayson wrote:

On 11/02/2024 08:41 PM, Chris M. Thomasson wrote:

On 11/2/2024 3:08 PM, Ross Finlayson wrote:

On 11/02/2024 01:22 PM, Chris M. Thomasson wrote:

On 11/2/2024 11:03 AM, Ross Finlayson wrote:

On 11/02/2024 06:54 AM, FromTheRafters wrote:

WM was thinking very hard :

On 01.11.2024 22:53, FromTheRafters wrote:

WM explained on 11/1/2024 :

On 01.11.2024 19:39, FromTheRafters wrote:

WM formulated the question :

>

Infinite subsets don't do that for you, even if you wish
really
hard.

>
They cannot evade if they are invariable.

>
Sets don't change.

>
Therefore the elements do not depend on us and our knowledge.
"If I
find x, then I can find x + 1" is not relevant. "For every x
(that I
find) there is x + 1" is no relevant. All elements are there,
independent of what we know or do. Therefore the first and the
last
are also there independent of us. If they weren't, their
existence
would depend on some circumstances and could change.

>
Circumstances like "there is no last element"?

>
That means, there is always another element. Potential infinity.

>
Sets don't change. Forget about amplifying 'not finite' with such as
'actual' and potential' -- infinite simply means not finite and
'actual/potential' is a distinction without a difference. A useless
concept outside of math philosophy.
>

the set of denominators have no largest element to 'start' with.

>
If all unit fractions are existing, then a smallest unit
fraction is
existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions
must
be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of
uncountably many points must be between 0 and x₀. That cannot
happen
at x₀ = 0.
>
Is that too hard to understand?

>
Apparently, for you.

>
Au contraire, there are multiple law(s) of large numbers,

>
What about this sucker (42^999429994299942) * 2 ?
>
Oh, don't forget about ((42^999429994299942) * 2) + 1   damn it!
>
>
>

and in mathematics like emergence after convergence,
the potential / practical / effective / actual distinction,
of "infinity", is a thing.
>
You know who discovered mathematics? Philosophers.
>
>

>

>
Well, I frame it about Cantor space, because, there are
some facts deducible from the asymptotic density of zero's
and one's, in the rows and columns Cantor space, even if
there are infinitely or trans-finitely many.

[...]
>
Cantor Pairing is fun. Mapping to and fro. Nothing is lost. WM disagrees
here, but shit happens.
>
>

>

>

>
Here's a way to think about it.

[...]
>
Cantor pairing works, and nothing is lost. That's that.
>

Numbering and counting ("pairing") are two different things,
much like order theory and set theory are two different things,
Cartesian and non-Cartesian functions are two different things,
ordinals and cardinals are two different things,
and non-Cartesian orderings in numberings are not pairings,
and won't be lost.
Don't get me wrong, I've lots experience with pairing, ...,
yet it works out that counting is not numbering,
and that counting does not suffice all cases of numbering.
Or, "Eudoxus/Cauchy/Dedekind is not sufficient",
though it's great for what it is,
it's not sufficient for a theory of everything,
and it's _not_ complete there.