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

On 10/30/24 11:38 AM, WM wrote:

On 29.10.2024 12:09, Richard Damon wrote:

On 10/29/24 4:42 AM, WM wrote:

 

NUF(x) MUST jump from 0 to Aleph_0 at all real values x, as below ANY real number x, there are Aleph_0 unit fractions.

 That is wrong. It holds only for the reals which you know: The definable reals.

No, it holds for ALL reals.
Your "undefinable numbers" are not real, but are fragments of the explosion of your reality into smithereens cause by the contradictions in your logic.
Logic can not work on things that are not defined, so you are just admitting that your arguements are not based on logic.

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No, but the first steps happen at undefinable x.

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No, it happens at an x that isn't a finite number.

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Then it is dark.

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And, as you said above, NOT REAL.

 A real number but not a definable real number.

But all real numbers are definiable, or they are not real numbers.

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If you allow your NUF to accept infintesimal numbers

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No, that is strongly forbidden.

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Then it just jumps.

 Believe what you like without foundation.
If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of not more than 1.
 Regards, WM

Nope, because there aren't "steps" to grow at, since no two points on the real axis are "adjacent"