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

On 10/7/24 8:38 PM, Chris M. Thomasson wrote:

On 10/7/2024 4:01 PM, Richard Damon wrote:

On 10/7/24 4:27 PM, Chris M. Thomasson wrote:

On 10/7/2024 4:17 AM, Richard Damon 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.

>
What do you mean? Are you trying to go the WM route where there is a largest natural number... We just can't see it yet because it's dark? Oh shit.

>
I am allowing that an INFINITE being MIGHT be able to comprehend something like an actual infinity. But this can not possibly be done by a finite being.

 Well, us as finite beings know that there is not a largest natural number... That right there is a basic understanding of the infinite: Fair enough?

Yes, us "smart" finite beings understand that the logic of there needing to be a "lowest value" unit fraction is incorrect, even if the "logic" of approaching the "existing" list of points from the low side would seem to imply that there should be a first.
We can't really "see" what is happening there, in a fixed creation point of view, which is what makes that concept not "real" for us.