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Why is a set of real numbers closed under addition?
Because adding any set of real numbers together will result in another real 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.
What does this mean Which set of these numbers is closed under division?
It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.
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.
Which set is closed under the operation multiplication?
Any set where the result of the multiplication of any two members of the set is also a member of the set. Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
