1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A new thought and a problem |P(A)| = 1?

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data


    P(A) = power set of A (in my book it is funky looking P, someone tell me how to read it and what it is)

    What is |A| and |P(A)|?

    a) A = [tex]\o[/tex]

    Book say that

    |A| = 0, and |P(A)| = 1

    Why?

    P(A) = {\o} I know that this is one thing (or one element), but the symbol represents empty set meaning nothing so

    {\o} = {{no elements}} = {}

    SO Why isn't |P(A)| = 0?

    EDIT: \o is supposed to be that symbol that looks like the greek letter phi, but I don't know why it isn't showing
     
  2. jcsd
  3. Sep 9, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can also write phi as {}. {} contains no elements. It's the empty set. |{}| means the number of elements in {}. That's 0. P({}) is the set of all subsets of {}. There's only one, {}. So P({})={{}}. It contains one element {}. So |{{}}|=1.
     
  4. Sep 10, 2011 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Do you mean this [itex]\mathcal{P}[/itex] ? use \mathcal{P}

    For [itex]\emptyset\,,[/itex] use \emptyset, although, \o does work for some implementations of LaTeX.
     
  5. Sep 10, 2011 #4
    Yes thank you lol, now I am wondering the heck is \o lol
     
  6. Sep 10, 2011 #5
    But {} is nothing
     
  7. Sep 10, 2011 #6
    Actually why is the empty set is a subset of A anyways?
     
  8. Sep 10, 2011 #7

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    It's not nothing. It's a set containing no elements. You can't just erase the curly brackets willy-nilly.
    It's because it's true that every element of the empty set is an element of A. Or to put it in a way that may be a little clearer, {} doesn't contain an element that is not also in A.
     
  9. Sep 10, 2011 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Try it this way. The empty set is like a bookcase containing no books. It's not nothing, it's still a bookcase.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A new thought and a problem |P(A)| = 1?
Loading...