Re: how

On 6/12/2024 2:27 PM, WM wrote:

Le 12/06/2024 à 20:18, Jim Burns a écrit :

On 6/11/2024 10:44 AM, WM wrote:

Le 10/06/2024 à 22:16, Jim Burns a écrit :

each natural number, defined or undefined,
has ℵ₀ followers.

>
No.
ℕ \ {1, 2, 3, ...} = ?
Where are  the followers?

>
Define
(Presume it is true that, when I say … , I mean … )

>
Simply name one.
>

ℕ \ {1, 2, 3, ...} = ?
Where are  the followers?

>
ℕ\{0,1,2,…}  =  ∅

>
So there are no followers?

there is no j ∈ ℕ after ℕ
ℕ = {y: ∀₃X⤾⁺¹₀:X∋y}
ℕ is the minimal inductive meta.set.
for each j ∈ ℕ
there are ℵ₀.many followers in ℕ
...because
there is NO j⁺¹ ∈ ℕ
WITHOUT 1.to.1 sⱼ∘f:{0<} → {j⁺¹<}
1.to.1 sⱼ:{j<} → {j⁺¹<}: sⱼ(k) = k⁺¹
1.to.1 f:{0<} → {j<}

Define

>
No. Simply answer.

Define
(Presume it is true that, when I say … , I mean … )
"No" == "Do not tell me (WM) what you mean"