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Re: Transitive
Posted:
Apr 26, 2014 2:24 PM


On Sat, 26 Apr 2014 02:09:36 0700, William Elliot <marsh@panix.com> wrote:
>On Sat, 26 Apr 2014, quasi wrote: >> William Elliot wrote: > >> >If A is a set, T a transitive set and A in T, is A transitive? >> Not necessarily. > >> Let x be an atom. >> Let T = {x,{x},{{x}}} and let A = {{x}}. >> Then T is transitive, and A is in T, but A is not transitive. > >Let x be the empty set. A isn't transitive. If y in A, then >y = {x} and y isn't a subset of A, because x in y but x not in A. > >So the answer is not always. > >Ordinals are hereditarily transitive. >Are there other hereditarily transitve sets?
http://en.wikipedia.org/wiki/Transitive_set
> >An hereditarily transitive set is a set for which every element >is an hereditarily transitive set.
Not quite...
> Is there a formal definition?
Do you have access to the internet?
http://en.wikipedia.org/wiki/Transitive_set
> >An hereditary set is a set for which every element >is an hereditary set. Is there a formal definition?



