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

Richard Damon expressed precisely :

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".

Indeed! If he had meant actually he should have put a comma as in:
Actually, infinite means infinite. IMO both versions are useless, just infinite with no modification. It is infinite if it is not finite.