Re: The set of necessary FISONs

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Sujet : Re: The set of necessary FISONs
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.math
Date : 11. Feb 2025, 10:31:48
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vof5e4$1n7gr$1@dont-email.me>
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
User-Agent : Mozilla Thunderbird
On 10.02.2025 16:16, Jim Burns wrote:
On 2/10/2025 4:56 AM, WM wrote:

The set of useless FISONs is inductive
and therefore infinite.
No FISON can change the assumption
U(A(n)) = ℕ.
Therefore every FISON can be omitted.
 Do you accept
∀ᴺj′:∀ᴺi′:∃ᴺk′:
  k′ = max{i′,j′+1}
?
No, I won't try to dive into your private notation. How induction works is well known. If not consult Wikipedia or my book
W. Mückenheim: "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin (2015)
The set F of FISONs which can be removed without changing the assumed result UF = ℕ is the infinite set F of all FISONs. This is proven by just the same induction as Zermelo proves his infinite set Z.
Either you accept both proofs or none. But without there is no set theory.
Regards, WM

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
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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
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27 Jan 25 i             `* Re: The set of necessary FISONs6joes
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28 Jan 25 i               +* Re: The set of necessary FISONs3joes
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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
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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
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27 Jan 25 i     i i i   i`* Re: The set of necessary FISONs8WM
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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
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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
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1 Feb 25 i     i i       i   `- Re: The set of necessary FISONs1joes
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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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