document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174659>Question 174659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following sets is closed under division?<BR>\n" );
document.write( "a. nonzero whole numbers <BR>\n" );
document.write( "b. nonzero integers<BR>\n" );
document.write( "c. nonzero even integers<BR>\n" );
document.write( "d. nonzero rational numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129686 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=129686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d) is the answer<BR>\n" );
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document.write( "Rational numbers are closed under addition, subtraction, multiplication, as well as division by a nonzero rational.\r<BR>\n" );
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document.write( "A set of elements is closed under an operation if, when you apply the <BR>\n" );
document.write( "operation to elements of the set, you always get another element of <BR>\n" );
document.write( "the set. \r<BR>\n" );
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document.write( "For example, the whole numbers are closed under addition, because if <BR>\n" );
document.write( "you add two whole numbers, you always get another whole number - there <BR>\n" );
document.write( "is no way to get anything else. \r<BR>\n" );
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document.write( "But the whole numbers are _not_ closed under subtraction, because you <BR>\n" );
document.write( "can subtract two whole numbers to get something that is not a whole <BR>\n" );
document.write( "number, e.g., \r<BR>\n" );
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document.write( "  2 - 5 = -3<BR>\n" );
document.write( " </SPAN>\n" );
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