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

On 19.09.2024 13:44, Richard Damon wrote:

On 9/19/24 7:22 AM, WM wrote:

On 19.09.2024 00:50, Richard Damon wrote:

On 9/18/24 8:33 AM, WM wrote:

On 15.09.2024 23:07, joes wrote:

Am Sun, 15 Sep 2024 21:52:30 +0200 schrieb WM:

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No definable points, to be precise. If there is no point next to 0 then
there is a gap. I do not accept gaps on the real line.

I.e. „neighbouring” points can’t be defined. There are no gaps.

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So it is.These points are dark.

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Nope, they just aren't.
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To be distinct points, there must be a gap, so they can not be neighboring,

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There are infinitely many points with no extension filling the space.

 Right, and none "next" to another, because there is always another in between them.

"always another" is potential infinity. I am discussing actual infinity where all are there at once and no "always" is used.

 

>

the space is filled by more points, creating smaller and smaller gaps

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That is potential infinity. In actual infinity all points are there at once.

 No, that is what infinity actually is. There are not two different "kinds" of it. All the point do exist, and we can express any of them.

Then you need no "always" but can point directly to the first point next to another.

The Infinite Set of these values actually exists, and all the values are in it,

that includes the first point of the interval and the second and so on.
Regards, WM