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When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Which set of numbers is closed under addition?
Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
Is the set of all complex numbers x that have absolute value 1 closed under multiplication?
of course!
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
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.
What sets of numbers are closed under addition?
Sets of numbers that are closed under addition include the integers, rational numbers, real numbers, and complex numbers. This means that when you add any two numbers from these sets, the result will also belong to the same set. For example, adding two integers will always result in another integer. This property is fundamental in mathematics and is essential for performing operations without leaving the set.
Are real numbers closed under addition?
yes because real numbers are any number ever made and they can be 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.
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 odd counting numbers closed for addition?
No.
Is there a subset of the natural numbers that is closed for addition?
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
Are the set of rational numbers closed under addition?
Yes, the set is closed.
