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

On 10/07/2024 05:38 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?

 Some have that there are _infinitely-grand_ natural integers,

that's just not "Archimedean", where the Archimedean property
of integers is "each finite yet as a whole in-finite".
 Then, some number theorists also indeed have a point at infinity.
I.e., a "point at infinity" "in the numbers".
 Of course I've mentioned that a bunch of times
so it's stupid to repeat trivialities especially
when they just get lost in a wash of ignorance.
 Anyways the numbers are as rich as they can be,
so saying they're not is sort of ignorant.
  I mean it's not as ignorant as committing gross crimes,
yet for some conscientious mathematicians, it's sort of
not quite up to the bar. (Of correct.)
 Then, it's not necessarily a crime against numbers
to not know or just ignore higher numbers, then
though of course that's at best "incomplete"
and what are otherwise accompanying conclusions,
would-be: completions, plain generalizations:
are un-sound.