On 2/11/2013 3:40 PM, Virgil wrote: > In article > <firstname.lastname@example.org>, > WM <email@example.com> wrote: > >> We show that the potentially infinite diagonal is in the list by >> proving that every o_nn is in the list. And every o that is in the >> list, is in some line of the list. And everything that is in some line >> of the list is in one line of the list. >> >> Anything wrong with this conclusion? > > Every member of a sequence can be in a list of members of sequences > without the sequence being in the list of sequences. > > Consider the list > L1 = 1, L2 = 2, L3 = 3 > Which does not contain D = 123 > even though every member of D is in one of L1 or L2 or L3 > > WM's claim is no more true than claiming that the union of a family of > sets must be one of the family being unioned. > > The union of all FISONs (finite initial segments of naturals) is not a > FISON. > > Given a list of all FISONs, the union of them is not a FISON. > Thus give a list of successively FISON-long strings, a string as long as > their union cannot be one of them. >
Whatever a "digit" in WMytheology is, I am unable to produce them to WM's satisfaction (it remains undefined).
By the same standard, is he not obligated to produce a list of successively FISON-long strings which include a string as long as their union? It has something to do with reality and existence. That is how the matter has been so painstakingly explained to me.