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.
Example:
√(-4) = 2i
-4 is real, 2i is complex.

5-3[x-7(x-6)]

To determine an example of real numbers that does not have a closure property for one of the basic operations, we need to consider an operation where combining two elements does not always result in a valid element within the same set.

Let's consider the square root operation (√) as an example. The square root of a non-negative real number is always a real number, but this operation does not have closure for negative numbers.

For instance, if we take the set of real numbers and perform the square root operation on any negative number, the result will no longer be a real number. This violates the closure property because combining two elements of the set (negative numbers) with the operation (√) does not always give us another element within the same set (real numbers).

Example:
Let's pick the number -4 as an example. The square root of -4 is denoted as √(-4). When we attempt to calculate this, we encounter a problem because the square root of a negative number is undefined in the set of real numbers. Therefore, √(-4) does not have closure under the square root operation in the set of real numbers.

In summary, the square root operation on negative real numbers is an example that does not have closure property within the set of real numbers.