No.
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.
No, the set of odd numbers is not closed under subtraction. For example, if you subtract one odd number from another odd number, such as 5 - 3, the result is 2, which is an even number and not part of the set of odd numbers. Therefore, the subtraction of odd numbers can yield results that fall outside the set.
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.
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.
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.
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: 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.