Q: Is a counting number closed under subtraction?

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

Yes they are closed under multiplication, addition, and subtraction.

Yes.

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.

Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".

Related questions

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

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 multiplication, addition, and subtraction.

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.

I Think is natural number a closed set under subtraction.

It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.

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

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.

Yes: Multiplying any two counting numbers will produce a counting number.

yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.

Yes.

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.