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!

Homework Help: The inverse of a set of points?

  1. May 5, 2004 #1
    I'm having trouble with this I'm sure it's a stupid terminology thing but for my personal retention, for example:

    what is the inverse of P (or mathematically put: p^-1)

    -thanks :biggrin:
  2. jcsd
  3. May 5, 2004 #2
    I'd guess it's a set without the points, or p={1/1, 1/2} i.e. p={1^-1, 2^-1}.
    It's more probable thats it's my second answer cos a set without 1 and 2 in its elements should be defined using the set-operation terms e.g. intersect, union (I forgot the one that means "without the elements")


  4. May 5, 2004 #3

    Chi Meson

    User Avatar
    Science Advisor
    Homework Helper

    I think it depends...

    A set of points (x,y) describes a position, and the inverse of a position does not have much meaning.

    The same set of points could, however, describe a displacement vector if the origin is assumed to be the initial location and (x,y) is the final location. The resultant displacement would have a magnitude of SQRT (x^2 + y^2) (that's pythagorean theorem), and this quantity could be inversed.

    There's probably other interpretations
  5. May 5, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper

    Without any extra context, the inverse of a set is not a meaningful concept.

    Meson - you're confusing sets with ordered pairs. Even so, ordered pairs are generally not considered to have inverses.

    Typically, inverses make sens used when you have:

    Binary operations and an identity e.g.:
    The multiplicative inverse of [tex]2[/tex] is [tex]\frac{1}{2}[/tex]. So [tex]2 \times \frac{1}{2} = 1[/tex]
    The additive inverse of [tex]2[/tex] is [tex]-2[/tex]. So [tex]2 + (-2) = 0 [/tex]

    Some type of relation:
    The inverse of [tex]f(x)=2x[/tex] is [tex]f^{-1}(x)=\frac{x}{2}[/tex]. For bijections this is also an inverse in the sense above. I.e. for [tex]f[/tex] a bijection, [tex]f(f^{-1}(x))=x[/tex] is the identity function, but can readily be generalized to relations, or so that the inverse of [tex]f:X \rightarrow Y[/tex], is [tex]f:Y \rightarrow P(X)[/tex] where [tex]P(X)[/tex] is the power set of [tex]X[/tex].

    There are probably other notions of inverse that I'm not thinking of. Regarding the notation [tex]P^{-1}[/tex] - I supose it might be used to describe the complement of [tex]P[/tex] but, if this is for a math course or text, look for the first instance of it in the text.
  6. May 5, 2004 #5
    ordered pairs do have inverses. The inverse of (1,3) is (3,1). Its just like with a function, to determine the inverse function you have to switch the x and y values.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook