[SOLVED] need help: uniquely encode two vectors from R^n into one vector in R^n

Hello,

first of all, Iīm not very experienced with mathematics, so please forgive me if I make statements which are unclear or not totally mathematical solid :)

my problem:

uniquely encode two vectors from R^n into one vector in R^n

After spending a lot of time in searching for possible solutions, I came up with the following:

let x,y be two vectors in R^n with x=(x1, x2, ..., xn) and y=(y1, y2, ..., yn)

the function f: R^n x R^n -> R^n , takes two vectors as parameters like this: f(x,y) and returns a new vector in R^n like this: f(x,y) = z

where z = (z1, z2, ..., zn)

every element of z is calculated using the following approach:

let zi be an element of z (with 1 <= i <= n), zi is created as a number in the open interval (0 ,1) by interleaving xi and yi

---> 0.xiyi

an example in R^2 would be:

x = (1 , 2)

y = (3 , 4)

z = (z1, z2)

z1 = 0.13 (created from x1 and y1)

z2 = 0.24 (created from x2 and y2)

so the question is: does this solution make sense ? is there a problem I donīt see ?

thank you,

Andreas