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Conjuction of sets

  1. Aug 2, 2008 #1
    If x [tex]\epsilon[/tex] A [tex]\subset[/tex] R[tex]\overline{}n[/tex] and y [tex]\epsilon[/tex] B [tex]\subset[/tex] R[tex]\overline{}m[/tex],

    then A X B [tex]\subset[/tex] R[tex]\overline{}m+n[/tex].

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

    thanks!

    (can't get the (m+n) above the line yet)
     
  2. jcsd
  3. Aug 3, 2008 #2
    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 [itex]R^{m+n}[/itex] and [itex]R^{(m+n)}[/itex], have never seen that notation.
     
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