Re: Replacement of Cardinality

On 8/30/24 9:08 AM, WM wrote:

Le 30/08/2024 à 03:09, Richard Damon a écrit :

On 8/29/24 9:27 AM, WM wrote:

Le 29/08/2024 à 01:48, Richard Damon a écrit :

On 8/28/24 8:57 AM, WM wrote:

Le 28/08/2024 à 04:13, Richard Damon a écrit :
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Well NUF(x) does not exist, but that doesn't say that infinity is not actual,

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So the unit fractions are actually existing but their number isn't? Strange!

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There number exists, it is aleph_0.
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You just can't count them from the "end" that doesn't have an end.

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Why not?
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Because you can't start at an end that isn't there.

 0 is below the end. Hence there is an end.

No, 0 IS the end that isn't a part of the set, since the set has now end on that side.

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Try to tell me the actual number you are going to start at.

 I start with NUF(0) = 0.

But then you can't move forward, as there can be no finite x such that NUF(x) is 1, since NUF(x/2) would need to be NUF(0) <= NUF(x/2) <= NUF(x), but there will be a unit fraction below x/2, and a unit fraction between x and x/2 (unless x >= 1) so NUF(x) can't be 1.

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Logic that depends on the existance of something that doesn't exist is just broken.

 Mathematics is the science which allows to prove things which cannot be seen.
 Regards, WM
 

Right, but can not be seen is not the same as doesn't exist.