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

On 10/16/2024 9:58 AM, WM wrote:

On 16.10.2024 18:09, FromTheRafters wrote:

WM formulated on Wednesday :

On 16.10.2024 13:54, Richard Damon wrote:

On 10/16/24 4:30 AM, WM wrote:

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There is a general rule not open to further discussion:
When doubling natural numbers we obtain even numbers which have not been doubled.
In potential infinity we obtain more even numbers than have been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
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But that isn't actually a general rule,

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It is a general rule that doubling creates larger numbers.

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It is a general rule that doubling finite cardinal numbers creates larger finite cardinal numbers.

 Yes.
 

In transfinite cardinalities Aleph_Zero times two is still Aleph_zero though.

 Here we talk only about natural numbers to be doubled.

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1*2=2
2*2=4
3*2=6
4*2=8
...
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2, 4, 6, 8, ...
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All natural numbers can be doubled, and they result in a natural number. Got it? It's simple.