document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771748>Question 771748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is (1, 1/2, 1/3, 1/4, 1/5, ...) closed under multiplication?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470407 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> CLosed under multiplication means that if you multiply any two elements (members) of the set together the answer (product) must be a member of the set. In the given set<BR>\n" );
document.write( "(1) A = {1,1/2, 1/3...} we have the identity one, which by definition will yield a product that is a member of the set. All of the other members of the set are of the form<BR>\n" );
document.write( "(2) 1/n or the inverse of a positive integer and when you multiply any two (or more) together you get<BR>\n" );
document.write( "(3) (1/n)*(1/m) = 1/(n*m) and since n*m is just another positive integer, the prduct of any of the other members is also a member of the set.<BR>\n" );
document.write( "Answer: Yes, the given set is closed under multiplication.<BR>\n" );
document.write( "Can you show that it is NOT closed under addition? subtraction? or division?  </SPAN>\n" );
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