Re: The set of necessary FISONs

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Sujet : Re: The set of necessary FISONs
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.math
Date : 01. Mar 2025, 18:47:32
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <7ac03d2e-5d72-4186-8b33-6fdddb7b83ff@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
User-Agent : Mozilla Thunderbird
On 3/1/2025 7:51 AM, WM wrote:
On 28.02.2025 20:25, Jim Burns wrote:
On 2/28/2025 12:04 PM, WM wrote:
On 28.02.2025 16:52, Jim Burns wrote:

An inductive proof only proves about
a set which is its.own.only.inductive.subset,
like Z₀ and like ℕ, perhaps not like Z
>
Z contains many inductive subsets.
>
(We don't know whether Z=Z₀ or Z≠Z₀)
>
Z contains every set a.
Zermelo describes set a as an element of Z
The claim
"Z contains every element of Z"
is not false, but
it isn't helpful, either.
https://en.wikipedia.org/wiki/Cooperative_principle
It's a claim which suggests that
what the words you use mean
is not what you think they mean.
https://www.youtube.com/watch?v=dTRKCXC0JFg

Z_0 contains only 0, {0}, {{0}}, ...
Z₀ = {0,{0},{{0}},...} is
the only subset of Z₀ which
holds 0 and, for each a, holds {a}
If the subset {i:A(i)} ⊆ Z₀ of k such that A(k)
is inductive,
then the subset {i:A(i)} = Z₀
By definition,
∀k ∈ {i:A(i)}: A(k)
{i:A(i)} = Z₀
∀k ∈ Z₀: A(k)
That universal claim did not come from a supertask.
It came from narrowing our focus from Z to Z₀.
In narrower Z₀,
inductivity identifies a unique set.

Consider this WM.inductive.proof:
>
It is sufficient
It is necessary

It is sufficient
for my purpose to consider
0, {0}, {{0}}, ...
which is an infinite set produced by induction.
https://www.youtube.com/watch?v=dTRKCXC0JFg

Date Sujet#  Auteur
21 Jan 25 * The set of necessary FISONs920WM
21 Jan 25 +* Re: The set of necessary FISONs51Richard Damon
21 Jan 25 i`* Re: The set of necessary FISONs50WM
22 Jan 25 i `* Re: The set of necessary FISONs49Richard Damon
22 Jan 25 i  `* Re: The set of necessary FISONs48WM
22 Jan 25 i   `* Re: The set of necessary FISONs47Richard Damon
22 Jan 25 i    `* Re: The set of necessary FISONs46WM
22 Jan 25 i     +* Re: The set of necessary FISONs2Python
23 Jan 25 i     i`- Re: The set of necessary FISONs1WM
23 Jan 25 i     `* Re: The set of necessary FISONs43Richard Damon
24 Jan 25 i      `* Re: The set of necessary FISONs42WM
24 Jan 25 i       `* Re: The set of necessary FISONs41Richard Damon
25 Jan 25 i        `* Re: The set of necessary FISONs40WM
25 Jan 25 i         +* Re: The set of necessary FISONs22joes
25 Jan 25 i         i+* Re: The set of necessary FISONs17Chris M. Thomasson
26 Jan 25 i         ii`* Re: The set of necessary FISONs16WM
26 Jan 25 i         ii +* Re: The set of necessary FISONs3joes
26 Jan 25 i         ii i`* Re: The set of necessary FISONs2WM
28 Jan 25 i         ii i `- Re: The set of necessary FISONs1Chris M. Thomasson
26 Jan 25 i         ii +* Re: The set of necessary FISONs7FromTheRafters
26 Jan 25 i         ii i`* Re: The set of necessary FISONs6WM
26 Jan 25 i         ii i `* Re: The set of necessary FISONs5FromTheRafters
27 Jan 25 i         ii i  `* Re: The set of necessary FISONs4WM
27 Jan 25 i         ii i   `* Re: The set of necessary FISONs3FromTheRafters
27 Jan 25 i         ii i    +- Re: The set of necessary FISONs1WM
28 Jan 25 i         ii i    `- Re: The set of necessary FISONs1Chris M. Thomasson
26 Jan 25 i         ii `* Re: The set of necessary FISONs5Chris M. Thomasson
26 Jan 25 i         ii  +- Re: The set of necessary FISONs1Chris M. Thomasson
27 Jan 25 i         ii  `* Re: The set of necessary FISONs3WM
27 Jan 25 i         ii   `* Re: The set of necessary FISONs2Richard Damon
28 Jan 25 i         ii    `- Re: The set of necessary FISONs1Chris M. Thomasson
26 Jan 25 i         i`* Re: The set of necessary FISONs4WM
26 Jan 25 i         i `* Re: The set of necessary FISONs3Richard Damon
26 Jan 25 i         i  `* Re: The set of necessary FISONs2WM
26 Jan 25 i         i   `- Re: The set of necessary FISONs1Richard Damon
25 Jan 25 i         `* Re: The set of necessary FISONs17Richard Damon
26 Jan 25 i          `* Re: The set of necessary FISONs16WM
26 Jan 25 i           +- Re: The set of necessary FISONs1joes
26 Jan 25 i           `* Re: The set of necessary FISONs14Richard Damon
26 Jan 25 i            `* Re: The set of necessary FISONs13WM
26 Jan 25 i             +* Re: The set of necessary FISONs6Richard Damon
27 Jan 25 i             i+* Re: The set of necessary FISONs4WM
27 Jan 25 i             ii+* Re: The set of necessary FISONs2FromTheRafters
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27 Jan 25 i             ii`- Re: The set of necessary FISONs1Richard Damon
28 Jan 25 i             i`- Re: The set of necessary FISONs1Chris M. Thomasson
27 Jan 25 i             `* Re: The set of necessary FISONs6joes
28 Jan 25 i              `* Re: The set of necessary FISONs5WM
28 Jan 25 i               +* Re: The set of necessary FISONs3joes
28 Jan 25 i               i`* Re: The set of necessary FISONs2WM
28 Jan 25 i               i `- Re: The set of necessary FISONs1Richard Damon
28 Jan 25 i               `- Re: The set of necessary FISONs1Richard Damon
21 Jan 25 +* Re: The set of necessary FISONs865Jim Burns
22 Jan 25 i`* Re: The set of necessary FISONs864WM
22 Jan 25 i `* Re: The set of necessary FISONs863Jim Burns
23 Jan 25 i  `* Re: The set of necessary FISONs862WM
23 Jan 25 i   `* Re: The set of necessary FISONs861Jim Burns
24 Jan 25 i    `* Re: The set of necessary FISONs860WM
24 Jan 25 i     +* Re: The set of necessary FISONs852Jim Burns
25 Jan 25 i     i`* Re: The set of necessary FISONs851WM
25 Jan 25 i     i +* Re: The set of necessary FISONs94joes
26 Jan 25 i     i i`* Re: The set of necessary FISONs93WM
26 Jan 25 i     i i +* Re: The set of necessary FISONs14joes
26 Jan 25 i     i i i`* Re: The set of necessary FISONs13WM
26 Jan 25 i     i i i `* Re: The set of necessary FISONs12joes
26 Jan 25 i     i i i  `* Re: The set of necessary FISONs11WM
26 Jan 25 i     i i i   +* Re: The set of necessary FISONs9joes
27 Jan 25 i     i i i   i`* Re: The set of necessary FISONs8WM
27 Jan 25 i     i i i   i +* Re: The set of necessary FISONs6joes
27 Jan 25 i     i i i   i i`* Re: The set of necessary FISONs5WM
27 Jan 25 i     i i i   i i +- Re: The set of necessary FISONs1joes
28 Jan 25 i     i i i   i i `* Re: The set of necessary FISONs3Richard Damon
28 Jan 25 i     i i i   i i  `* Re: The set of necessary FISONs2WM
28 Jan 25 i     i i i   i i   `- Re: The set of necessary FISONs1Richard Damon
27 Jan 25 i     i i i   i `- Re: The set of necessary FISONs1Richard Damon
26 Jan 25 i     i i i   `- Re: The set of necessary FISONs1Richard Damon
26 Jan 25 i     i i `* Re: The set of necessary FISONs78Richard Damon
26 Jan 25 i     i i  `* Re: The set of necessary FISONs77WM
26 Jan 25 i     i i   `* Re: The set of necessary FISONs76Richard Damon
27 Jan 25 i     i i    `* Re: The set of necessary FISONs75WM
27 Jan 25 i     i i     +- Re: The set of necessary FISONs1Richard Damon
27 Jan 25 i     i i     `* Re: The set of necessary FISONs73joes
27 Jan 25 i     i i      `* Re: The set of necessary FISONs72WM
27 Jan 25 i     i i       +* Re: The set of necessary FISONs18FromTheRafters
28 Jan 25 i     i i       i`* Re: The set of necessary FISONs17WM
28 Jan 25 i     i i       i +* Re: The set of necessary FISONs12FromTheRafters
28 Jan 25 i     i i       i i`* Re: The set of necessary FISONs11WM
28 Jan 25 i     i i       i i +* Re: The set of necessary FISONs6FromTheRafters
28 Jan 25 i     i i       i i i`* Re: The set of necessary FISONs5WM
28 Jan 25 i     i i       i i i +* Re: The set of necessary FISONs3FromTheRafters
29 Jan 25 i     i i       i i i i`* Re: The set of necessary FISONs2WM
29 Jan 25 i     i i       i i i i `- Re: The set of necessary FISONs1Richard Damon
31 Jan 25 i     i i       i i i `- Re: The set of necessary FISONs1joes
28 Jan 25 i     i i       i i `* Re: The set of necessary FISONs4joes
28 Jan 25 i     i i       i i  `* Re: The set of necessary FISONs3WM
28 Jan 25 i     i i       i i   `* Re: The set of necessary FISONs2joes
28 Jan 25 i     i i       i i    `- Re: The set of necessary FISONs1WM
31 Jan 25 i     i i       i `* Re: The set of necessary FISONs4joes
1 Feb 25 i     i i       i  `* Re: The set of necessary FISONs3WM
1 Feb 25 i     i i       i   +- Re: The set of necessary FISONs1Richard Damon
1 Feb 25 i     i i       i   `- Re: The set of necessary FISONs1joes
27 Jan 25 i     i i       +* Re: The set of necessary FISONs44joes
28 Jan 25 i     i i       `* Re: The set of necessary FISONs9Richard Damon
25 Jan 25 i     i `* Re: The set of necessary FISONs756Jim Burns
26 Jan 25 i     `* Re: The set of necessary FISONs7joes
26 Jan 25 `* Re: The set of necessary FISONs3Richard Damon

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