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

On 10/2/24 7:57 AM, WM wrote:

On 02.10.2024 13:17, Richard Damon wrote:

On 10/1/24 1:39 PM, WM wrote:

On 01.10.2024 01:14, Richard Damon wrote:

On 9/30/24 11:15 AM, WM wrote:

On 30.09.2024 00:29, FromTheRafters wrote:

WM explained on 9/29/2024 :

On 28.09.2024 00:08, FromTheRafters wrote:
 > WM presented the following explanation :
>
 >> Between two unit fractions there is always a finite gap.
 >
 > How big?
>
In terms of set theory: uncountably many points.

>
How wide are these points?

>
More than nothing.

>
But it must be next to nothing,

>
No, between them and nothing there are infinitely many countable sets and then finite sets of points.

>
So your "smallest" wasn't the smallest,

 Of course all gaps between unit fractions are made of more than finitely many points. I never denied that.

But that also means that no point are "next to" each other.

 

which becomes nothing when we get to the actual infinite set.

>
Not in mathematics.

>
Sure it does.

 Try to learn the basics and to understand ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

Which means that for all n that are in the Natural numbers, for the unit fraction  1/n, theree DOES EXIST another unit fraction 1/(n+1) that is smaller than it.
Thus, *NO* unit fraction can be found to be the smallest. EVER, not even "Dark" as if your dark number are members of the Natural Numbers as you claim, they must still follow that property, since you claim it for *ALL* Natural numbers.
Sorry, your logic is just blown to smithereens by its inconsistencies.

 Regards, WMK