# Algebra 2

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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.

• Algebra 2 -

2011/0 is not real number

• Algebra 2 -

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.

• Algebra 2 -

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

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