Re: The set of necessary FISONs

On 2/27/25 5:53 AM, WM wrote:

On 27.02.2025 05:06, Richard Damon wrote:
 

And where does that use the term "Induction"

 He does not use the term but the matter: { } and with a also {a}.
 Regards, WM
 

So, you admit that you are just misquoting the source, which is a LIE.
That sort of behavior normally causes an Academic to lose face and position, but I guess you don't have any of that left, as you have been totally discredited,
What Cantor does is use a method parallel to induction to construct the set, with the axiom that there is a starting point, and an axiom that for every item there is a following item, and an axiom that an infinite set is allowed, to get to the results that allows the axiom of induction to say that if the domain of the true value of a predicate being true includes 0, and the value following every value that results in true, also results in true, then the predicate is true for all Natural Numbers.
That parallel method is NOT induction, but is just a natural result of iterating the successor axiom an infinite number of times (something we, as a finite being can't do, so we need to imagine that the system can just do it, thus the need of the infinity axiom).
Your problem is you forget that this level of mathematics is based on the idea that we have assumed that infinite processes can complete in the system, even though we can't do it, and your "finite logic" that assumes only what we can do, can't be used in such a system.
Yes, at any finite point in the iteration, the set build so far has a maximum element, but when we let the process complete (even though we can't do it) the result changes to not have a maximum element.
Of course, you call that assumption a Mathology, trying to degrade it, but it is the core for letting Mathematics break out of the finite shell of our existance.