Conjuction of sets

1. Aug 2, 2008

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)

2. Aug 3, 2008

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.