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The inverse of a set of points? 
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#1
May504, 06:57 AM

P: 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 


#2
May504, 07:29 AM

P: 309

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 setoperation 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? 


#3
May504, 09:53 AM

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P: 1,772

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 


#4
May504, 04:32 PM

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P: 2,538

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


#5
May504, 04:35 PM

P: 299

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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