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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Wed, 5 Mar 2025 09:24:22 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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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.

-- 
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.