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For a set to be closed under an operation, doing the operations on any two members of the set must result in another member of the set.
The set of even natural numbers is {2, 4, 6, ...}.
When two even numbers are added, the result is also an even number.
Adding two positive numbers results in a larger positive number.
Thus, adding two even natural numbers together results in another even natural number and so is closed.
The set of even whole numbers is {..., -6, -4, -2, 0, 2, 4, 6, ...}.
When two even numbers are added, the result is also an even number.
It does not matter which combination of positive and negative whole numbers are added as all positive and negative whole numbers (including zero) are in the set. Thus it is also closed under addition.
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Why are natural numbers not under addition?
Natural numbers are actually closed under addition. If you add any two if them, the result will always be another natural number.
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.
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 natural numbers closed under addition?
Yes, when you add any group of natural numbers, the sum will also be a natural number.
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.
Under which operation are natural numbers closed?
Addition.
Why are natural numbers not under addition?
Natural numbers are actually closed under addition. If you add any two if them, the result will always be another natural number.
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.
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.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Is the set of natural numbers closed under addition?
Yes, when you add any group of natural numbers, the sum will also be a natural number.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Are natural numbers closed under addition?
Yes, because naturals are counting numbers, {1,2,3...} and any natural number added by another natural number has to be a natural. Think of a number line, and your adding the natural numbers. The sum has to be natural, so yes it is closed.
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.
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
