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Q: Why regular languages are not closed under infinite union?
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What are the closure properties of regular sets?

;: Th. Closed under union, concatenation, and Kleene closure. ;: Th. Closed under complementation: If L is regular, then is regular. ;: Th. Intersection: .


Is a rational number closed under addition?

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.


What is closed and not-closed under addition?

The set of even numbers is closed under addition, the set of odd numbers is not.


When are complex numbers closed under addition?

Quite simply, they are closed under addition. No "when".


Why are odd integers closed under multiplication but not under addition?

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.


Are polynomial expressions closed under subtraction?

Yes they are closed under multiplication, addition, and subtraction.


Are rational numbers closed under subtraction?

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.


Are rational numbers closed under division multiplication addition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.


Is the collection of integers closed under subraction?

Yes, the set of integers is closed under subtraction.


What is a set of rational numbers not closed under?

It is not closed under taking square (or other even) roots.


Why is zero not closed under the operation of whole numbers?

A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.


Is the set of composite number closed under multiplication?

Is { 0, 20 } closed under multiplication