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On 20.10.2024 14:20, Alan Mackenzie wrote:It also doesn't mean accessible to intuition. What you like to call logic, is merely your intuition which seems to be malfunctioning.
> WM <wolfgang.mueckenheim@tha.de> wrote:
>
>> Say mapping or multiplying, it is a process. But that is not important.
>> Important is only that in the image there are numbers which have not
>> been mapped because 2n > n.
>
> That "because" attempts to connect two unrelated statements there are no
> "numbers which have not been mapped". If you think there are, give an
> example.
>
They can be proven by mathematics: Density reduced, fixed number, interval enlarged.
>> If this is not accepted, then not all natural numbers of the image have
>> been in the original set.
>
> <Sigh>. The sets are infinite.
>
Infinite does not mean inaccessible to logic.
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