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On 11.03.2025 23:51, Jim Burns wrote:On 3/11/2025 5:28 PM, WM wrote:On 11.03.2025 20:25, Jim Burns wrote:On 3/11/2025 2:01 PM, WM wrote:
...which isn't>>Zermelo defines Z to be an inductive set.>
in order to ensure the existence of
an infinite or inductive set.
No.
Um aber die Existenz "unendlicher" Mengen zu sichern,
bedürfen wir noch des folgenden ... Axioms.
[Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266]
⎛ Menge Z, welche die Nullmenge als Element enthält undThere is a definition and there is an axiom.>
Where are they?
Please quote a definition
which is outside of the axiom.Your advice to Zermelo would be to write
A definition answers "What is Z ?"They are different kinds of things.>
And you are unable to understand the connection
between these two things.
Is it the language?"If it was a snake, it'd have bit me."
Or is it a general deficit?
>The definition of Z states that>
Z is inductive.
Please quote this definition which
is not the axiom.
Thank you.>in order to ensure the existence of>
an infinite or inductive set.
A definition doesn't ensure existence.
That's what an axiom does.
This axiom
This axiom ensures the sequence of numbers"The same induction" is NOT
by the same induction
which ensures the dark numbers:...your darkᵂᴹ numbers about which
which ensures the dark numbers:Since what follows is NOT
{} ∈ Z₀, and for all x: if x ∈ Z₀ then {x} ∈ Z₀
ℕ \ F(1) = ℵo,
and if
ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n) = ℵo
then
ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n+1) = ℵo.
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