Question 520538
The set of whole numbers is closed under subtraction.True or false?
<pre>
The whole numbers are {0,1,2,3,...}

False, because you can subtract your way out of the set of whole 
numbers. For instance take the two whole numbers 2 and 5.  If you 
subtract  2 - 5 you get a negative number -3, and no negative numbers 
are whole numbers.  So you've subtracted your way out of the set of 
whole numbers.
</pre>
The set of integers is closed under multiplication.  True or false?
<pre>
True, because you can't multiply your way out of the set of integers.
If you multiply an integer by an integer, you will always get another 
integer.
</pre>
The set of integers is closed under division.True or false?
<pre>
False, because you can divide your way out of the set of integers.
For instance if you divide the integer 1 by 2 you get {{{1/2}}}, which
is not an integer.  So you've divided your way out of the set of 
integers. 

Edwin</pre>