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

On 10/7/24 8:35 PM, Chris M. Thomasson wrote:

On 10/7/2024 3:58 PM, Richard Damon wrote:

On 10/7/24 7:44 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:".

>
But all his reference to the word "Actually" are part of his trying to define the term "Actual Infinity".
>

>
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?
>

>
It implies that there exists a first positive real, rational number or unit fraction for one (at least the way WM uses it).

 A first unit fraction would be 1/1? :^) However this is in the very _strict_ realm of unit fractions. WM seems to like to mix and match realms. Not sure why he thinks there is a smallest unit fraction... Anyway, shit happens.

No, because he IS specifying the direction of counting, and is trying to count from the "end" that doesn't have an end.
His view is that if the values of the existing unit fractions exist, and we travel up the line from the negative side in increasing value, it on.y make sense that there should be a "first" point we reach.
The concept, on the face of it, seems logical, it just is a fact that it doesn't work, and that is in part because of some of the strange properties that trying to imagine a realized infinity creates.