Re: The set of necessary FISONs

Am Tue, 04 Mar 2025 20:56:17 +0100 schrieb WM:

On 04.03.2025 17:43, Jim Burns wrote:

On 3/4/2025 5:49 AM, WM wrote:

 

Here is only *one* argument standing for a long while.

The union ⋃{F} of FISONs and the intersection ⋂𝒫ⁱⁿᵈ of inductive
subsets are the same set.

Correct. You need not the intersection however because Z₀ can also be
defined by { } ∈ Z₀, and if {{{...{{{ }}}...}}} with n curly brackets ∈
Z₀ then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀.

 
Your (WM's) darkᵂᴹ numbers are bracketed by ⋂𝒫ⁱⁿᵈ and ⋃{F}

No, they are following. Every induction surpasses every finite number
but never all finite numbers. It is always a finite number.

No. That is why you use induction instead of directly proving the finite
number of sentences.

Cantor's N however is larger: [...]

Therefore ℕ is more than UF.
By induction like Zermelo we find:
∀n ∈ U(F): |ℕ \ {1, 2, 3, ..., n}| = ℵo.

What we don't find: |N \ U{F(n): n e N}| = Aleph_0,
because it is in fact wrong.

⎛ ⋂𝒫ⁱⁿᵈ = ⋃{F}

True.

⎜ Mehdi Hasan, a British journalist, suggests using ⎜ three steps to
beat the Gish gallop:

I need only one step: I delete your gibberish without addressing it and
put the topic.

That is called sealioning, I believe.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.