Re: The set of necessary FISONs

On 2/8/2025 2:44 PM, WM wrote:

On 08.02.2025 12:51, Richard Damon wrote:

And thus you claim that 36 can not be factored,
as all of its factors are not needed.

>
1, 2, 3, 4, 6, 9, 12, 18, 36.
According to Cantor,
the set of factors has a smallest element,

Also, according to Pythagoras.
The proof that √2 is irrational
derives a contradiction from the assumption that
there exists a denominator q: q⋅√2 ∈ ℕ  and thus
there must be a smallest denominator q₀: q₀⋅√2 ∈ ℕ
and a smaller.than.smallest denominator q₋₁
⎛ p₀² = 2q₀²
⎜ (2p₋₁)²/2 = q₀²
⎝ p₋₁² = (2q₋₁)²/2

the set of factors has a smallest element, 1, and
the set of necessary factors has a smallest element, 6,
or if double application is not allowed, 4.

What is an unnecessary factor?

 Regards, WM