LudovicoVan
Posts:
3,800
From:
London
Registered:
2/8/08


Re: set builder notation
Posted:
Aug 17, 2013 12:25 PM


<lite.on.beta@gmail.com> wrote in message news:3f6ee20284004a989582f164f5ed51a0@googlegroups.com... > > S = {x /in A  P(x) } > > For the set builder notation above, what we really means is: > > all things x, such that "x is element of A *and* P(x) is true" correct? > > The vertical bar is essentially conjunction, correct?
No, there is no such thing as "all things x" with no further qualification. Where you find S = { x  P(x) }, it is a notational simplification where the universe of discourse, i.e. the ambient set, is obvious and implied. For example, all *real* x such that, all *apples* x such that, etc. etc.
Julio

