Re: The set of necessary FISONs

On 2/14/2025 7:55 AM, WM wrote:

On 13.02.2025 19:16, Jim Burns wrote:

On 2/13/2025 6:59 AM, WM wrote:

All of us who know induction
know that
by induction we have obtained that
all FISONs

>
each FISON

>
No, all FISONs.

Each FISON F′ is in
the only inductive subset {F} of the set of
all FISONs: {F}
Proving that
{F:visibleᵂᴹ} ⊆ {F} is any inductive subset
is
proving that
{F:visibleᵂᴹ} is the only inductive subset {F}
is
proving that
{F:visibleᵂᴹ} = {F}
is
proving that
each FISON F′ is visibleᵂᴹ
Proving that
{F:visibleᵂᴹ} ⊆ {F} is any inductive subset
is NOT proving that
☠( {F} is visibleᵂᴹ.

The set of all natural numbers
is proved by induction, not the set of each natural number.

Each natural number is in
the only inductive subset of the set of
all natural numbers.
The set of all natural numbers is not.in
the only inductive subset of the set of
all natural numbers.

The present topics are "What is induction?"

>
No, everybody not knowing it, like you,
should first learn it.