Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 11/29/24 2:28 PM, WM wrote:

On 29.11.2024 19:56, Richard Damon wrote:

On 11/29/24 12:38 PM, WM wrote:

 

Set theory says that the sets ℕ = {1, 2, 3, ...} and D = {10n | n ∈ ℕ} can be bijected by clever mapping. That means there are as many n as 10n as black hats. That means by clever shifting the black hats they will cover all n.

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Yep, that's what it says, and it is true.
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Note, NOTHING in that statement talks about working with finite subset of those sets,

 That's why set theory is in contradiction with mathematics.

No, YOUR INCORRECT "MATHEMATICS" based on your incorrect assumptions is in contradiction to set theory, which is very much consistant with mathematics, since modern mathematics is based on set theory as a foundation.

So, you are just shown to be using the logic of lies.

 Analysis is no a lie.

Bad Analysis, like what you do is.

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Nothing in set theory talks about the equivalence of properties of the infinite set to the properties of the finite sets

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That is the field of analysis. I believe that application of analysis provides correct results for the infinite.

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Apparently your concept of it doesn't, because you are using broken rules,

 No, I am using a very simple and sound rule. If all hats of finite intervals (0, n] fail to cover more than 1/10, then it is impossible to cover more than 1/10 of the whole set ℕ because beyond all finite intervals and all finite n, there is no supply of black hats. Even a moderate brain should see that.

So, you admit to MAKING UP your rules based on your own ideas, even when they re proven to be incorrect.
All you are doing is proving that your logic, based on the INCOPRRECT ASSUMPTION, that infinte sets are just like finite sets, just bigger, is just incorrect.
Your logic, which seems to be just naive "mathematics", has exactly the same sort of problem that naive set theory had, that by not having a firm foundation, it was able to run into contradictions which broke it.

 Regards, WM
    maybe because you don't actually understand how to do analysis.

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Sorry, starting from lies just gets you more lies.
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Regards, WM

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