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

Am Mon, 14 Oct 2024 15:37:13 +0200 schrieb WM:

On 14.10.2024 14:02, joes wrote:

Am Mon, 14 Oct 2024 12:28:58 +0200 schrieb WM:

On 12.10.2024 22:47, Richard Damon wrote:

On 10/12/24 2:55 PM, WM wrote:

>

2n > n. That holds for all finite numbers. It halves the density.

And half of infinity is infinity.

The density of the natural umbers is 1 number per place, the density
of the doubled numbers is 1/2 number per place.

And there being inf. many places, that makes both amounts infinite.

Neither 1 nor 1/2 are infinite. These values are calculated by all
finite subsets of the set and in the limit.

The amount of numbers in G and N. You cannot make an infinite set
finite by only taking every second number. A subset cannot have
more elements than the parent.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.