document.write( "Question 253313: under which operations is the set(1,2,3,....) closed? \n" ); document.write( "

Algebra.Com's Answer #185606 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
under which operations is the set(1,2,3,....) closed?
\n" ); document.write( "

\r\n" );
document.write( "If you ADD two numbers in the set, you always get another \r\n" );
document.write( "number ii the set. For instance if you ADD 3 + 5, which \r\n" );
document.write( "are both in the set, you get 8 which is ALSO in the set.\r\n" );
document.write( "You CANNOT ADD your way out of the set.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, it's closed under ADDITION.\r\n" );
document.write( "\r\n" );
document.write( "If you SUBTRACT two numbers in the set, you DON'T always \r\n" );
document.write( "get another number in the set.  For instance if you SUBTRACT \r\n" );
document.write( "3 - 5, which are both in the set, you get -2 which is NOT \r\n" );
document.write( "in the set.  So you CAN SUBTRACT your way out of the set.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, it's NOT closed under SUBTRACTION.\r\n" );
document.write( "\r\n" );
document.write( "If you MULTIPLY two numbers in the set, you always get another \r\n" );
document.write( "number in the set.  For instance if you MULTIPLY 3 x 5, which \r\n" );
document.write( "are both in the set, you get 15 which is also in the set.  So \r\n" );
document.write( "you CANNOT MULTIPLY your way out of the set.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, it's closed under MULTIPLICATION.\r\n" );
document.write( "\r\n" );
document.write( "If you DIVIDE two numbers in the set, you DON'T always get \r\n" );
document.write( "another number in the set.  For instance if you DIVIDE 3 ÷ 5, \r\n" );
document.write( "which are both in the set, you get the fraction  which \r\n" );
document.write( "is NOT in the set.  So you CAN DIVIDE your way out of the set.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, it's NOT closed under DIVISION.\r\n" );
document.write( "\r\n" );
document.write( "If you EXPONENTIATE two numbers in the set, you always get another \r\n" );
document.write( "number in the set.  For instance if you EXPONENTIATE , \r\n" );
document.write( "which are both in the set, you get 16 which is also in the set.  \r\n" );
document.write( "So you CANNOT EXPONENTIATE your way out of the set.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, it's closed under EXPONENTIATION.\r\n" );
document.write( "\r\n" );
document.write( "So it's CLOSED under ADDITION, MULTIPLICATION, and EXPONENTIATION.\r\n" );
document.write( "\r\n" );
document.write( "It is NOT CLOSED under SUBTRACTION or DIVISION.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );