Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,340
Registered: 5/20/10
Re: set builder notation
Posted: Aug 17, 2013 7:34 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Saturday, August 17, 2013 4:12:34 AM UTC-7, lite.o...@gmail.com wrote:
> 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, consider

S = { x /in A | P(a,b,x,y,z) }




there is an implicit ALL(x)
by placing x on the left of the bar.


x is no longer free in P


the conjunction A&B
just returns a value of true or false.


S = {x | p(x)}

is shorthand for

ALL(x) xeS <-> p(x)



Putting complex expressions before the bar is a different shorthand...

it's really


S = { x | xeA & P(x) }




Set Specification increases the level of the logic above FOL.

Now you can solve S UNION T

using the pre-designated parameter in p(...)



X e ( S U T ) <- X e S
X e ( S U T ) <- X e T


so to test for UNION it will then backward chain to
a direct element check on one or both of the unioned sets

...via how they were specified... and then call p()

X e S <- p(X)


Herc

--
www.phpPROLOG.com

www.tinyurl.com/How-Prolog-Works




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.