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Q: Are natural numbers closed for subtraction?

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No.A set is closed under subtraction if when you subtract any two numbers in the set, the answer is always a member of the set.The natural numbers are 1,2,3,4, ... If you subtract 5 from 3 the answer is -2 which is not a natural number.

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

No.

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No.A set is closed under subtraction if when you subtract any two numbers in the set, the answer is always a member of the set.The natural numbers are 1,2,3,4, ... If you subtract 5 from 3 the answer is -2 which is not a natural number.

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.

Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.

No.

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

You can give hundreds of examples, but a single counterexample shows that natural numbers are NOT closed under subtraction or division. For example, 1 - 2 is NOT a natural number, and 1 / 2 is NOT a natural number.

While natural numbers are closed with respect to addition and mulitplication, they are missing the additive identity (zero). Furthermore, they are not closed with respect to two of the fundamental operations of arithmetic: subtraction and division.

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

Yes, they are.

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.

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

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