Sujet : Re: The set of necessary FISONs
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 03. Mar 2025, 21:06:33
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <a2a8323c-dad3-4ac0-a7fc-621e088f6044@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 3/3/2025 12:58 PM, WM wrote:
On 03.03.2025 18:01, FromTheRafters wrote:
Discrete elements.
>
Yes, of course:
{ }, {{ }}, {{{ }}}, ...
This is the sequence of numbers.
That's Z₀
⎛ ... Die Menge Z₀ enthält
⎜ die Elemente 0, {0}, {{0}}, usw.
⎝ und möge als "Zahlenreihe" bezeichnet werden, ...
⎛ ... The set Z₀ contains
⎜ the elements 0, {0}, {{0}}, etc.
⎝ and may be referred to as a "number series", ...
According to Zermelo its existence guarantees
the set of numbers Z₀ = {{ }, {{ }}, {{{ }}}, ...}.
It is the existence of
an indefinite set Z such that
0 ∈ Z ∧ ∀a: a ∈ Z ⇒ {a} ∈ Z
which guarantees the existence of
the definite set Z₀ which is
its.own.only.inductive.subset.
We do not construct[make] Z₀
We construct[know] Z₀
----
If we insist on having an analogy over there at
that human activity which leaves us with
roads and bridges and skyscrapers and homes,
construction.as.title.insurance
might be better than
construction.as.pounding.nails.
https://en.wikipedia.org/wiki/Title_insuranceTitle insurance is intended to guarantee that,
if you proceed with a purchase of land,
the documents alleging that you will own it
are valid and will convey ownership to you.
Construction[proof] of the real numbers
is intended to guarantee that there is, in fact,
such a thing as ℝ
ℝ ⇄ {S⊆ℚ:(ℚ\S)ᵉᵃᶜʰ>ᵉᵃᶜʰSᵉᵃᶜʰ<ₛₒₘₑS}\{{},ℚ}
doesn't make anything.
Neither does title insurance.
That doesn't make them unimportant.