Conjunction of Sets: x,y in Rm+n vs Vector z in R(m+n)

[krcmd1]

If x \epsilon A \subset R\overline{}n and y \epsilon B \subset R\overline{}m,

then A X B \subset R\overline{}m+n.

Is there any difference between the connotation of (x,y) \epsilon R\overline{}m+n and a vector z in R\overline{}(m+n)?

thanks!

(can't get the (m+n) above the line yet)

 

[mrandersdk]

the short answer is no. But this is because when the notation is like that, it is clearly isomorphic. That is to every z there is a unique (x,y) and the other way around.

Don't know why you distinguish between R^{m+n} and R^{(m+n)}, have never seen that notation.