Re: The set of necessary FISONs

On 08.02.2025 23:18, Jim Burns wrote:

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.

Hippasos found it and was treated with hostility by the Pythagoreans. I taught it about 40 times. There is no denominator follwing upon infinitely many.

 

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?

That is a factor which is needed to obtain the product 36. When going through the sequence, all factors can be dropped till the last that is necessary. 2*18 is not necessary because 4*9 follows afterwards.
Regards, WM