posted by JOY on .
Need help PLEASE!! Question is:
There is no Closure Property of Division that applies to Integers. For example 2 divided by 3 is not an interger. What is another example of real numbers that does not have a Closure Property for one of the basic operations? Give an example to illustrate your claim.
2011/0 is not real number
If we restrict ourselves to positive integers, then subtraction does not have a closure property, for example:
5-7=-2 ∉ N.
If we are dealing with real numbers, division does not have closure property, because we cannot divide by zero.
On the other hand, non-zero real numbers are closed under division.
Real numbers are not closed under square-root, because the square-root of a negative number is complex.
√(-4) = 2i
-4 is real, 2i is complex.