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Is a set of natural numbers a group under the operation of addition?
No, a set of natural numbers is not a group under the operation of addition. For a set to be a group, it must satisfy four properties: closure, associativity, identity, and inverses. While the natural numbers are closed under addition and associative, there is no additive identity (0 is not included in the natural numbers) and no inverses (there is no natural number that can be added to another natural number to yield zero).
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.
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.
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 the number of protons plus the number of neutrons in an atom always a whole number?
The two are counts and so natural numbers. The set of natural numbers is closed under addition.
Under which operation are natural numbers closed?
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.
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.
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.
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.
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.
What is the number of protons plus the number of neutrons in an atom always a whole number?
The two are counts and so natural numbers. The set of natural numbers is closed under addition.
Is closure a property of natural numbers?
Yes, closure is a property of natural numbers. In mathematics, a set is said to be closed under an operation if performing that operation on members of the set always produces a member of the same set. For example, the set of natural numbers is closed under addition and multiplication, as the sum or product of any two natural numbers is always a natural number. However, it is not closed under subtraction or division, as these operations can yield results that are not natural numbers.
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".
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.
What operations are natural numbers closed?
Addition and multiplication.
