Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/28/24 5:09 AM, WM wrote:

On 28.11.2024 01:30, Richard Damon wrote:

On 11/27/24 4:43 PM, WM wrote:

On 27.11.2024 22:14, Richard Damon wrote:

On 11/27/24 2:15 PM, WM wrote:

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It it the successor for the SET of natural numbers.

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And that is nothing else but all natural numbers.

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No, the set is different from its members.

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By what?

 

It is a set, with set type properties, and its members are Natural Numbers, with Natural Number like propertis.
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The set is equal to N, which is the name of the set, but none of the members are 'equal' to N, they are MEMBERS of it.

 The members together are ℕ.
The collection of definable natnumbers is ℕ_def.
The collection of all natnumbers is ℕ.
 Regards, WM

But since all the members of N are definable, your N_def actually is N.
Now, if you are crippled enough in your logic that keeps you from understanding big numbers, so you think your N_def is something else, that is just on you, and not a problem with the Natural Numbers.
All you have shown is that your logic of finite numbers can not handle the actual infinite set of Natural Numbers, or even actually define your finite subset of them N_def, so N_def is just itself a contradiction, which has blown your brain to smithereens with its contradictions.
You are unable to actually DEFINE what your N_def actually is, making your logic just a lie.