The inverse of a set of points?

[thinice]

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:

[quddusaliquddus]

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?

[Chi Meson]

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

[NateTG]

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


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

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 2 is \frac{1}{2}. So 2 \times \frac{1}{2} = 1
or
The additive inverse of 2 is -2. So 2 + (-2) = 0

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

There are probably other notions of inverse that I'm not thinking of. Regarding the notation P^{-1} - I supose it might be used to describe the complement of P but, if this is for a math course or text, look for the first instance of it in the text.

[Parth Dave]

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.