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The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set.
26 is a positive whole number.
40 is a positive whole number.
However 26-40 = -14 which is clearly not a positive whole number. So positive whole numbers are not closed under subtraction.
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Under what operation is the set of positive rational numbers not closed?
Subtraction.
Which sets of numbers are closed under subtraction?
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.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Give ten examples of natural number are closed under subtraction and 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.
What sets of numbers are closed under addition?
Sets of numbers that are closed under addition include the integers, rational numbers, real numbers, and complex numbers. This means that when you add any two numbers from these sets, the result will also belong to the same set. For example, adding two integers will always result in another integer. This property is fundamental in mathematics and is essential for performing operations without leaving the set.
Under what operation is the set of positive rational numbers not closed?
Subtraction.
Which sets of numbers are closed under subtraction?
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.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Which set of numbers is closed under subtraction?
A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
What does this mean Which set of these numbers is closed under subtraction?
It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5
Is the set of integers closed under subtraction?
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.
Are rational numbers closed under division multiplication addition or subtraction?
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.
True or False The set of whole numbers is closed under subtraction Why?
False. The set of whole numbers is not closed under subtraction. Closure under subtraction means that when you subtract two whole numbers, the result is also a whole number. However, this is not always the case with whole numbers. For example, subtracting 5 from 3 results in -2, which is not a whole number.
Are rational numbers closed under subtraction operation?
Yes, they are.
Are real numbers closed under addition and subtraction?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
Is the set of real numbers closed under addition?
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Is the set of whole numbers closed 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.
