The inverse of a set of points?

  1. I'm having trouble with this I'm sure it's a stupid terminology thing but for my personal retention, for example:
    p={1,2}

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

    -thanks :biggrin:
     
  2. jcsd
  3. 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")

    I MIGHT BE COMPLETELY WRONG! SO WAIT TILL SUM1 WHO KNOWS ANSWER FOR SURE COMES ALONG.

    ok?
     
  4. Chi Meson

    Chi Meson 1,772
    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. NateTG

    NateTG 2,537
    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]
    or
    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. 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.
     
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