document.write( "Question 174659: Which of the following sets is closed under division?
\n" ); document.write( "a. nonzero whole numbers
\n" ); document.write( "b. nonzero integers
\n" ); document.write( "c. nonzero even integers
\n" ); document.write( "d. nonzero rational numbers \n" ); document.write( "

Algebra.Com's Answer #129685 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Which of the following sets is closed under division?
\n" ); document.write( "a. nonzero whole numbers
\n" ); document.write( "

\r\n" );
document.write( "No, it's not closed because it's possible to divide our \r\n" );
document.write( "way out of the set of whole numbers. For example we can \r\n" );
document.write( "start with two nonzero whole numbers, say 5 and 2, and \r\n" );
document.write( "divide them and get 2.5, which is NOT a whole number. \r\n" );
document.write( "So we have divided our way out of the set of whole \r\n" );
document.write( "numbers.  Since this is possible, the set of\r\n" );
document.write( "nonzero whole numbers is not closed under division.\r\n" );
document.write( "

\n" ); document.write( "b. nonzero integers
\n" ); document.write( "

\r\n" );
document.write( "No, it's not closed, for non-zero whole numbers are \r\n" );
document.write( "nonzero integers, and the above example shows that \r\n" );
document.write( "it's not closed.\r\n" );
document.write( "

\n" ); document.write( "c. nonzero even integers
\n" ); document.write( "

\r\n" );
document.write( "No because it's possible to divide our way out of the set of\r\n" );
document.write( "nonzero even integers. For example we can start with two nonzero\r\n" );
document.write( "even integers, say 8 and 6, and divide them and get , which\r\n" );
document.write( "is NOT a nonzero even integer. So we have divided our way out of the\r\n" );
document.write( "set of nonzero even integers.  Since this is possible, the set of\r\n" );
document.write( "nonzero even integers is not closed under division.\r\n" );
document.write( "

\n" ); document.write( "d. nonzero rational numbers
\n" ); document.write( "

\r\n" );
document.write( "Yes because it is impossible to divide our way out of the set of\r\n" );
document.write( "nonzero rational numbers. For example we can start with two nonzero\r\n" );
document.write( "rational numbers, say  and , which is indeed a nonzero rational number. So we cannot \r\n" );
document.write( "divide our way out of the set of nonzero rational numbers.  Since this \r\n" );
document.write( "is not possible, the set of nonzero rational numbers is indeed closed \r\n" );
document.write( "under division.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );