Question 521101
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.


---------------------------


For a set to be <u>closed under subtraction</u>, 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 <u>closed under subtraction</u>


For example, the set of integers is closed under subtraction since subtracting ANY two integers gives you an integer.



---------------------------



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)


If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com">jim_thompson5910@hotmail.com</a>


Also, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Thank you


Jim