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

On 10/8/24 3:30 PM, Chris M. Thomasson wrote:

On 10/7/2024 5:57 PM, Richard Damon wrote:

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.

 Humm... Well, I know that there is no smallest unit fraction, yet there are infinitely many of them that get closer and closer to zero, yet never reach it because no unit fraction will ever actually equal zero. That right there helps me as a finite being to understand some basic facts about infinity. And yes, WM, actual infinity... ;^)

Yes, and we understand that by understanding the process of potential infinity, that for each number there is a smaller number.
In the "Actual Infinity" the numbers are all there so it would seem by logic that there needs to be a smallest one, but there isn't.
Because we just can't imagine how that would work, because the rules of the infinite are different than what we are used to perceiving.