Re: 2N=E

On 01.11.2024 13:37, FromTheRafters wrote:

WM laid this down on his screen :

On 01.11.2024 11:59, FromTheRafters wrote:

WM used his keyboard to write :

On 31.10.2024 22:53, FromTheRafters wrote:

WM pretended :

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Our sets do not change.

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Then:
Multiplication of all infinitely many fractions of the open interval (0, 1) results in some fractions in (1, 2).
Multiplication of all infinitely many numbers of the open interval (0, ω) result in some numbers in (ω, ω*2).

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No, there are no finite numbers in the transfinites.

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Numbers like ω + 4 are in the infinite. But if all natural numbers are doubled, then numbers in the infinite are produced.

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What makes you think so?

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Simplest mathematics. Doubling increases the value. If all natnumbers are existing, then the greatest existing natnumber is existing too,

 That is not the nature of the set of natural numbers. There is no last, that is for finite sets only.

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But there are all. No point can escape doubling.

 

then doubling it does not produce a natural number.

 Stemming from a bad assumption, any garbage can be claimed.

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Yes, Cantor's theory is the best example.

 

Actual infinity is not about variable sets!

 Sets don't change!

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Therefore not all doubled elements can be absorbed by the set.