On Nov 3, 2:13 pm, Gus Gassmann <horand.gassm...@googlemail.com> wrote: > On Nov 3, 8:47 am, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > On Nov 3, 7:53 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 3 Nov., 11:39, William Hughes <wpihug...@gmail.com> wrote: > > > > > On Nov 3, 6:10 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > On 3 Nov., 04:38, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > So what. You do not need a new element to make a new set > > > > > > > > of elements. > > > > > > > > If it is not possible to drop an element of an existing set, then you > > > > > > > need a new element in order to have a new set. > > > > > > > Nope, this does not hold in general or for "linear" sequences of sets. > > > > > > You do not need to drop an element or add an element to get > > > > > > a new set.- > > > > > > That sounds interesting! You drop extensionality? > > > > > Nope. You do not need to drop an element or add an element to geta new > > > > set from the elements in a collection of more than one set (if the > > > > collection > > > > is "linear" then it cannot have a largest set). > > > > That is not interesting but simply a wrong claim. You can learn that > > > here:http://en.wikipedia.org/wiki/Axiom_of_extensionality > > > > Regards, WM > > > Nope > > > Theroem: > > > You do not need to drop an element or add an element to get a new set > > from > > the elements in a collection of sets without largest set. > > > Proof. > > > Let C be the collection and I an index set. > > Let K be the new set. > > If x in C_i (i in I) then x in K or x is dropped. > > Therefore K contains union over I (C_i) > > However, no element is added so K contained in Union over I (C_i) > > K must be Union over I (C_i) > > C does not have a largest set so K is not in C. > > > K is defined by its elements. > > x in K iff x in C_j for some j in I > > It seems the Great Professor Mueckenheim does not know the difference > between equality of two sets and the union over a countable > collection. Eight years of intense studies of set theory can do that > to a man, you know. Cut him some slack.-
A tiny correction: eight years of intense studies of set theory __with a huge a priori bias (we may call it prejudice) and a very poor basis in basic mathematics__ can do that to a man.
