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

On 20.10.2024 16:18, WM wrote:
 > On 20.10.2024 14:56, Alan Mackenzie wrote:
 >> WM <wolfgang.mueckenheim@tha.de> wrote:
 >
 >>>>> The only alternative is that doubling numbers creates only doubled
 >>>>> numbers.
 >>
 >>>> That's more or less what happens, except that numbers aren't "created".
 >>>> They just are.
 >>
 >>> That's not what happens in mathematics.
 >>
 >> How would you know?
 >
 > I know that 2n > n.
 >
 >>> The mapping needs larger numbers than have been mapped.
 >>
 >> It does not.  Each number in the image is in the range.
 >
 > Impossible. The density is halved in the image, the number of elements
 > is the same, therefore the image is twice as large and half of its
 > numbers are not in the original set.
 >
 > Regards, WM