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

Am Thu, 17 Oct 2024 20:22:12 +0200 schrieb WM:

On 17.10.2024 00:39, Jim Burns wrote:
 

No natural number is the first to not.have a natural.number.double.

True.

Aha!

When doubling all natural numbers we obtain only natural numbers.

That is impossible.

Contradiction to your agreement below.

There is no first natural number from which we obtain (by doubling)
anything not.a.natural.number.

True.

Thus, your "dark" numbers can't be natural.

The only set of natural numbers with no first is the empty set..

No, the set of dark numbers is another set without smallest element.

You mean, like the unit fractions?

There is no ▒▒▒▒▒ natural number from which we obtain (by doubling)
anything not.a.natural.number.

[spam snipped]

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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.