You have forgotten that if A1 and non-A1 are indeed complements of each other in set A, and so are A1 and A2, then necessarily non-A1 = A2 (and non-A2 = A1). Thus A1 + non-A1 + A2 + non-A2 = (A1 + non-A2) + (A2 + non-A1) = (A1 + A1) + (A2 + A2) = A1 + A2 = A. So saying A = A1 + A2 is equivalent to saying A = A1 + non-A1 + A2 + non-A2, with the only difference being that one form is redundant.
On Sat, Mar 2, 2013 at 9:28 PM, Piaget Modeler <[email protected]>wrote: > > It appears that A is redefined: A = A1 + non-A1 + A2 + non-A2 > > So A1 is no longer A non-A2 but something else? > > ~PM > > ------------------------------ > Date: Sat, 2 Mar 2013 21:13:26 -0600 > Subject: Re: [agi] What if non-A was an entity? > From: [email protected] > To: [email protected] > > > How would this change anything? > > > On Sat, Mar 2, 2013 at 8:21 PM, Piaget Modeler > <[email protected]>wrote: > > > I'm looking at some literature right now, and am having a mental puzzle. > > In a classic Euler or Venn Diagram when we have a circle denoted A, the > space outside the circle typically represents not-A. > (see Attachment 1 - affirmations & negations #1). > > Consequently if we suppose A is comprised of A1 and A2 (i.e., A = A1 + > A2), and we say that A1 = A non-A2 or if we say > that A2 = A non-A1, we are looking at negative space, and subtracting > either A1 or A2 from the set A (see Attachment 2 > - affirmations & negations #4). > > Suppose we make non-A1 and non-A2 explicit (see Attachment 3 - > affirmations & negations #5). How does this change things? > What does A = A1 + A2 now mean? > > Your thoughts? > > ~PM > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/23050605-2da819ff> | > Modify <https://www.listbox.com/member/?&;> Your Subscription > <http://www.listbox.com> > > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/19999924-5cfde295> | > Modify <https://www.listbox.com/member/?&;> Your Subscription > <http://www.listbox.com> > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/23050605-2da819ff> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
