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

On 10/10/24 2:53 PM, WM wrote:

On 10.10.2024 20:45, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

 

If all natnumbers are there and if 2n is greater than n, then the
doubled numbers do not fit into ℕ.

>
For any finite n greater than zero, 2n is greater than n.  The same
does not hold for infinite n.

 There are no infinite n = natural numbers.
 

Numbers multiplied by 2 do not remain unchanged. That is not intuition
but mathematics.

>

True,

>

Fine, then you can follow the above discussion. Either doubling creates
new natural numbers. Then not all have been doubled. Or all have been
doubled, then some products fall outside of ℕ.

>
No.  Not even close.

 Deplorable. But note that all natural numbers are finite and follow this law: When doubled then 2n > n. If a set of natural numbers is doubled, then the results cover a larger set than before.
 Regards, WM
 

You might think so, but that ignores the laws of mathematics of infinite values.
The SIZE of the set of natural numbers is infinite, and thus obeys the laws of infinite numbers. An infinite number, which has a finite number, added to, multiplied by, or used as a power, is still that same infinite number. It may seem impossible, but that is the nature of infinite numbers.