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What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Are negative numbers closed under addition?
Negative numbers are not closed under addition. When you add two negative numbers together, the result is always a negative number, which fits the definition of closure. However, if you add a negative number and a positive number, the result can be either positive, negative, or zero, thus violating the closure property for negative numbers. Therefore, negative numbers alone are not closed under addition.
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.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
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.
Is the set of real numbers closed under addition?
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Are real numbers closed under addition?
yes because real numbers are any number ever made and they can be closed under addition
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.
Under which operation are natural numbers closed?
Addition.
Are the rational numbers closed under addition?
Yes.
Is the set of irrational numbers closed under addition?
no it is not
Is the set of odd numbers closed under addition?
no
