Re: The set of necessary FISONs

On 2/4/25 5:50 AM, WM wrote:

On 04.02.2025 01:39, Richard Damon wrote:

On 2/3/25 7:45 AM, WM wrote:

On 02.02.2025 21:11, Richard Damon wrote:

On 2/2/25 11:39 AM, WM wrote:

describe the set ℕ?

N is not a natural number.

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Not described by the Peano axioms?

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You seem to not understand the differnce between a number and a set of numbers

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Peano creates by induction the set ℕ of all natural numbers.
Why doe I not delete by the same induction the set of all FISONs?

 

Because you don't prove the needed induction.
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You prove that no individual F(n) is needed.

 F(1) can be subtracted, and if F(n) can be subtracted, then F(n+1) can be subtracted. That is the needed induction.

Which just proves that all F(n) are in the set that can be individually not needed.
That doesn't prove your requirments, that we don't need to use some combination.
As I showed before, we can build N by the union of two disjoint sets of FISONs, therefore no individual FISON can be individually necessary, that doesn't mean that we can't build up the set N by the union of some infinite set of FISONs.
As I also showed, you logic also says that we can not factor 36, as on factor of 36 is necessary, but that is absurd, of course we can factor 36, many ways: 1 x 36, 2x18, 3x12, 4x9, 6x6, 2x2x9, 2x3x6, 2x2x3x3
There is no item in common to all of these, so none is necessary, but the operation can be done.
You are just too stupid to see the flaw in you logic, or even to recognize the flaw when pointed out, because you mind is just colapsed into a black hole from the gigantic explosion from the contradictions in your logic, leaving a big pile of NOTHING.

Note also, Peano doesn't "create" the Naturals with induction,

 He does. 1 or 0 ∈ ℕ, and if n is there, then n' is there.

Which doesn't CREATE the set N, it shows that some other set is N.
I guess you just don't understand the statement.
N was created by the other Axioms, not the induction axiom, that is how we can TEST if some set is N.

 Regards, WM