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Topic: set builder notation
Replies: 12   Last Post: Aug 24, 2013 1:38 AM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: set builder notation
Posted: Aug 17, 2013 12:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

<lite.on.beta@gmail.com> wrote in message
news:3f6ee202-8400-4a98-9582-f164f5ed51a0@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





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