Q: Why are natural numbers not under addition?

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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.

Yes, when you add any group of natural numbers, the sum will also be a natural number.

Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.

The two are counts and so natural numbers. The set of natural numbers is closed under addition.

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

Related questions

Addition.

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

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.

Yes, when you add any group of natural numbers, the sum will also be a natural number.

Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all 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.

The two are counts and so natural numbers. The set of natural numbers is closed under addition.

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

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

No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.

Addition and multiplication.

yes because real numbers are any number ever made and they can be closed under addition