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

On 10/19/24 5:24 AM, WM wrote:

On 18.10.2024 03:26, Richard Damon wrote:

On 10/17/24 2:46 PM, WM wrote:

On 17.10.2024 02:18, Richard Damon wrote:

On 10/16/24 1:18 PM, WM wrote:

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Of course it is a general rule. Doubling creates larger numbers.

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But those numbers are still in the set, and all the members of the set were doubled, so none of the doubled values got us to a value that wasn't doubled.

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Therefore not all doubles are natural.

 

So, what ones aren't?

 They all are dark and cannot be named individually.

So which ones are those?
It seems your set of Natural Numbers wasn't complete to begin with, as every Natural Numbers is namable individually.

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It is proven that the set of Natural Numbers are closed under multiplication.

 That is not the set but the potentially infinite collection of Peano numbers.

Which is what builds the actual infinite set. "Actual Infinity" is what you get when you conplete that construction process.
If you don't conplete it, you don't get an actual infinity.

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Regards, WM