On 15 Jun., 21:03, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > WM says... > > >On 15 Jun., 18:46, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: > >> I'm not sure what you are saying. The fact is, we can prove > >> that for every real r_n on the list, d is not equal to r_n. > > >Of course. Every real r_n belongs to a finite initial segment of the > >list. > >That does not yield any result about the whole list > > On the contrary, the definition of "d is on the list" > is that "there exists a natural number n such that r_n = d".
You make it too easy.
r_n = d would mean that there is a finite list containing d.
> We proved "forall n, r_n is not equal to d". So that > means "there does not exist a natural number n such that r_n = d", > so that means "d is not on the list". > > We have thus proved something about the whole list.
Wrong. You proved something for every finite list. Like for every finite set: |{2, 4, 6,..., 2n}| is not larger than each of its elements. In the same way you may prove that Hercules' list does not contain pi and (!!!) that every single line that contains all digits of Hercules' list 3.1415 and so on in infinity does not contain pi. You are very inconsequent, always changing the meaning of for all.
> You have to actually learn logic to be able to tell the difference.
No, one has only to become a set theorist and parrot every nonsense of that sad "theory".
