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

On 10/07/2024 04:44 AM, Alan Mackenzie wrote:

Richard Damon <richard@damon-family.org> wrote:

On 10/7/24 7:13 AM, joes wrote:

Am Mon, 07 Oct 2024 10:13:21 +0200 schrieb WM:

On 06.10.2024 17:55, joes wrote:

Am Sun, 06 Oct 2024 17:26:07 +0200 schrieb WM:

On 06.10.2024 16:52, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

>

This idea of time may be what misleads the mathematically less adept
into believing that 0.999... < 1.

That is true even in actual infinity.
We can add 9 to 0.999...999 to obtain 9.999...999. But multiplying
0.999...999 by 10 or, what is the same, shifting the digits 9 by one
step to the left-hand side, does not increase their number but leaves
it constant: 9.99...9990.
10*0.999...999 = 9.99...9990 = 9 + 0.99...9990 < 9 + 0.999...999 ==>
9*0.999...999 < 9 as it should be.

In actual infinity, there is no last 9 (that would not be infinite).

Actual means all, but not more. This implies a last before ω. The
infinity means an end cannot be determined. It is produced by the dark
numbers.

Actually infinite means infinite, which doesn’t change when you add or
subtract a finite number.

>
>

Actual infinity doesn't exist for us finite beings.

>
English language tip: The "Actually" in that sentence was not attached to
the word "infinite", it meant something like "This is really true:".
>
Anyhow, what do you mean when you say that "actual infinity doesn't
exist"?  I think we established over the weekend that for a mathematical
entity not to exist, it must cause a contradiction.  Or something like
that.
>
So what contradiction would the existence of actual infinity cause?
>

Sure it does, for stronger mathematical platonists,
an "absolute infinity" is yet another mathematical ideal,
and what reason and phenomenology tells us is that we're
finite beings and may "attain" to the actual infinite
or absolute infinite, and that it is a sublime thing.
For example, Kant, gives most all of scientism any
of its credence with respect to the critique of judgment,
being all phenomenological while the platonistic ideal
as existing yet as noumenological, as, "Sublime", furthermore,
the "more than itself" part, it's said to exist.
Actual infinity exists despite us finite beings.