Sujet : Re: The set of necessary FISONs
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 06. Mar 2025, 14:47:12
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <f9746399-8cdd-455a-93b0-1ec746b74dbf@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
User-Agent : Mozilla Thunderbird
On 3/6/2025 4:15 AM, WM wrote:
Am 06.03.2025 um 10:06 schrieb joes:
Am Wed, 05 Mar 2025 22:05:04 +0100 schrieb WM:
Therefore iterartion fails to produce
actual infinity.
>
As an element, but not as
the number of elements (=the size of the set).
We do NOT construct[make] sets.
We construct[know] sets.
We construct[know] by induction only sets which
are their own only.inductive.subset.
We do NOT construct[know] by induction sets which
we don't KNOW are their own only.inductive.subset,
not even if we know they're inductive.
The number of elements is an element
for every element produced by induction.
For each element in a set which
is its.own.only.inductive.subset,
that element's set of priors has
fuller.by.one sets which are larger.
Wrong.
Of course induction "is infinite".
UF is not empty.
Induction is potentially infinite.
Proof.by.induction completes at the end of
the finite sequence of finite.length claims
(each claim true.or.not.first.false)
which claims that the subset.of.interest
(of a set its.own.only.inductive.subset)
is an inductive subset.
Never an actually infinite set is porduced.
Your actually infinite sets hold elements
about which it.cannot.be.said they self.equal.
They will not be missed.