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!

Characteristic function and preimage?

  1. Sep 20, 2012 #1
    Characteristic function and preimage???

    1. The problem statement, all variables and given/known data

    Let S be a nonempty subset of ℝ.

    Define χs= { 1 if x is in S and 0 if x is not in S

    Determine χs-1(Q) [where Q=set of all rational numbers]

    and χs-1((0,∞))

    We haven't really dealt much with this function, and I really don't know how to go about doing this. I'm guessing for Q it will be all x in S such that f(x)=Q? Is that right?

    Any help is appreciated,

    Thanks.
     
  2. jcsd
  3. Sep 20, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Characteristic function and preimage???

    Then go back an review the definitions! Once you know the definitions, this problem is trivial.

    Your function, "[itex]X_S[/itex]" (strictly speaking, "[itex]\chi_s[/itex]", the Greek letter "chi") is defined to be 1 if x is in S, 0 if not. In other words, the only possible value of x is 0 or 1, both of which are rational numbers, but only 1 is in [itex](0, \infty)[/itex].
     
  4. Sep 20, 2012 #3
    Re: Characteristic function and preimage???

    Thank you, so for the rationals, the preimage of chi sub s is the set of all numbers in S and the complement of S, i.e. the set of all reals. Is that correct?
     
  5. Sep 20, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Re: Characteristic function and preimage???

    Yes.

    (There are no numbers which are both in set S and in the compliment of set S.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Characteristic function and preimage?
Loading...