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

On 10/20/2024 11:51 AM, Chris M. Thomasson wrote:

On 10/20/2024 12:48 AM, WM wrote:

On 20.10.2024 00:54, Jim Burns wrote:

On 10/19/2024 2:19 PM, WM wrote:

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A doubled finite is finite.

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If all finites are doubled, then not all results can be in that set.

 Sigh.

{ 1, 2, 3, 4, 5, 6, ... }
{ 1*2, 2*2, 3*2, ... }
All the doubled numbers are already in the set of naturals:
{ 2, 4, 6, ... }
{ 1, (2), 3, (4), 5, (6), ... }
See?

 

Either more finites appear, or the results are infinite.

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No k exists such that
2⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.

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All doubled numbers result in larger numbers. That cannot be avoided.
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Regards, WM