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

On 10/20/2024 12:39 PM, WM wrote:

On 20.10.2024 21:30, Richard Damon wrote:
 

No, the alternative is that infinite sets work like infinite sets without an end, and that this means that some of the properties of finite sets don't hold for infinite sets.
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When the density is reduced and the number remains the same, then the size is increased. Not accepting this means violating mathematics.

density? Would you agree that the reals are more dense than the unit fractions?
Are you referring to:
{ 2, 4, 6, ... }
With the gap being two instead of one as in:
{ 1, 2, 3, ... }
2 - 1, 3 - 2, ... gap 1 vs
4 - 2, 6 - 4, ... gap 2?
Keep in mind:
{ 1*2, 2*2, 3*2, ... }
Notice how all the naturals are in there? 1 2 3 and 2 4 and 6, they are all naturals!