document.write( "Question 521101: My question is \" the set of whole numbers is closed under subtraction. if false, give a counterexample.\" First what are whole number? And what does it mean by closed under subtraction \n" ); document.write( "
Algebra.Com's Answer #346340 by jim_thompson5910(35256)\"\" \"About 
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The set of whole numbers is the set {0, 1, 2, 3, 4, 5, 6, ...}\r
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\n" ); document.write( "\n" ); document.write( "This is the set of positive integers (ie numbers that have no decimal/fractional part) with zero included.\r
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\n" ); document.write( "\n" ); document.write( "For a set to be closed under subtraction, EVERY possible subtraction of ANY two elements must lie in the set. So if you subtract ANY two elements in a certain set, and that result is also in the same set, then that set is closed under subtraction\r
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\n" ); document.write( "\n" ); document.write( "For example, the set of integers is closed under subtraction since subtracting ANY two integers gives you an integer.\r
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\n" ); document.write( "\n" ); document.write( "Using this info, we'll find that the statement \"the set of whole numbers is closed under subtraction\" is false since 0 - 2 = -2 (this is the counterexample)\r
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\n" ); document.write( "\n" ); document.write( "Notice we're subtracting 2 from 0 (both of which are whole numbers) to get -2 (which is NOT a whole number)\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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