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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
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The set of whole numbers is the set {0, 1, 2, 3, 4, 5, 6, ...}
This is the set of positive integers (ie numbers that have no decimal/fractional part) with zero included.
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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
For example, the set of integers is closed under subtraction since subtracting ANY two integers gives you an integer.
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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)
Notice we're subtracting 2 from 0 (both of which are whole numbers) to get -2 (which is NOT a whole number)
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Jim
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