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

On 10/31/24 1:41 PM, WM wrote:

On 31.10.2024 13:22, Jim Burns wrote:

On 10/31/2024 4:13 AM, WM wrote:

 

Neither
  ∀n ∈ ℕ: 1/n - 1/(n+1) > 0
nor
  ∀ᴿx > 0: ∀n ∈ ℕ: ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
is wrong.

>
But the first formula predicts that
only single unit fractions
are existing on the real line.
How could NUF(x) grow from zero by more than 1?

>
Is
⎛  ∀ᴿx > 0:
⎜  ∀n ∈ ℕ:
⎝ ⅟⌈n+⅟x⌉ ∈ ⅟ℕ∩(0,x]
wrong?

 One of two contradicting formulas must be dropped.
Regards, WM
 

Or, just admit that your NUF(x) is where the contradiction is and drop it.
But then you lose the basis of your logic, so you are stuck with the fact that you logic is just contradictory and has blown itself up to smithereens by trying to use finite logic on infinite sets.