document.write( "Question 991505: Give an example for non zero real numbers is not closed under subtraction r \n" ); document.write( "

Algebra.Com's Answer #611360 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
by definition, if the operation produces even one element outside of the set, the operation is $\"not\"$ closed \r
\n" ); document.write( "\n" ); document.write( "set of natural numbers $\"N\"$ is $\"NOT\"$ closed under subtraction\r
\n" ); document.write( "\n" ); document.write( "example: let $\"a=3\"$ and $\"b=5\"$ , then $\"a-b=3-5=+-2\"$ => $\"-2\"$ is $\"NOT\"$ element of $\"N\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"N\"$ is subset of the set of real numbers $\"R\"$ \r
\n" ); document.write( "\n" ); document.write( "note:
\n" ); document.write( "Real Numbers include:
\n" ); document.write( "Whole Numbers (like $\"0\"$ , $\"1\"$ , $\"2\"$ , $\"3\"$ , $\"4\"$ , etc)
\n" ); document.write( "Rational Numbers (like $\"3%2F4\"$ , $\"0.125\"$ , $\"0.333\"$ ..., $\"1.1\"$ , etc )
\n" ); document.write( "Irrational Numbers (like $\"pi\"$ , sqrt(3), etc )\r
\n" ); document.write( "\n" ); document.write( "One subset of Real Numbers is counting (or natural) numbers. This subset includes all the numbers we count with starting with \" $\"1\"$ \" to infinity. The subset would look like this:\r
\n" ); document.write( "\n" ); document.write( "{ $\"1\"$ , $\"2\"$ , $\"+3\"$ , $\"4\"$ , $\"5\"$ ...}\r
\n" ); document.write( "\n" ); document.write( "Another subset is whole numbers. This subset is exactly like the subset of counting numbers, with the addition of one extra number. This extra number is \" $\"0\"$ \". The subset would look like this:\r
\n" ); document.write( "\n" ); document.write( "{ $\"0\"$ , $\"1\"$ , $\"2\"$ , $\"+3\"$ , $\"4\"$ , $\"5\"$ ...}\r
\n" ); document.write( "\n" ); document.write( "so, your answer is set $\"N\"$ or you can choose set of whole numbers\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );