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What is a counterexample to the set of negative numbers is closed under subtraction?
Wiki User
∙ 10y ago
-2 - (-5) = -2 + +5 = +3. (+3 is not in the set of negative numbers.)
Wiki User
∙ 10y ago
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What is an example of a counterexample for the difference of two whole numbers is a whole number?
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
Is the whole number closed under subtraction?
If you interpret "whole numbers" as "integers", then yes. If you interpret "whole numbers" as "non-negative integers", then no.
Are the prime numbers closed for subtraction?
No.
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
What is the set of whole numbers closed by?
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
What is an example of a counterexample for the difference of two whole numbers is a whole number?
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
Is the set of irrational numbers closed under 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.
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.
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.
Is the whole number closed under subtraction?
If you interpret "whole numbers" as "integers", then yes. If you interpret "whole numbers" as "non-negative integers", then no.
Are the prime numbers closed for subtraction?
No.
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 .
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
What is the set of whole numbers closed by?
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
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.
