Re: The set of necessary FISONs

On 2/22/25 7:35 AM, WM wrote:

On 22.02.2025 13:13, FromTheRafters wrote:

WM formulated on Saturday :

On 22.02.2025 12:14, FromTheRafters wrote:

WM explained on 2/22/2025 :

On 22.02.2025 02:05, Richard Damon wrote:

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Note, as I understand it, that initial Zermelo Set Theory didn't even HAVE "induction",

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You don't understand it.

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He understands it better than you do apparently. Zermelo's theory didn't have transfinite induction.

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Who claimed that?

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Certainly not you.

 Only stupids could do so.
 

First element and the successor function is induction.
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First element and successor function is 'inductive hypothesis' not induction.

 Nonsense. The inductive step is proved in my example from |ℕ \ {1, 2, 3, ..., n}| = ℵo, i.e., by several axioms, and in Zermelo's example by a single axiom.
 Regards, WM

Which just proves that no specific FISON is individually REQURED to make the set of Natural Numbers.
Which doesn't prove anything, unless you want to admit that the number 36 can't be factored because none of the factors are required factors.
Sorry, you are just showing you are too stupid to understand what you are talking about.
And that ignores the fact that you just admitted you don't know what "induction" is, and are just using the wrong word, likely because you don't actually understand what the concept of it actually is, as it does require an understanding of what infinity actually is, which you have shown to be beyond your ability.