Study guides

☆☆

Q: Are sets of fractions closed under addition?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Yes.

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.

Yes

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".

Closed sets and open sets, or finite and infinite sets.

Related questions

Yes.

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.

Yes

I know that whole numbers, integers, negative numbers, positive numbers, and even numbers are. Anyone feel free to correct me.

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".

;: Th. Closed under union, concatenation, and Kleene closure. ;: Th. Closed under complementation: If L is regular, then is regular. ;: Th. Intersection: .

Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.

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.

Closed sets and open sets, or finite and infinite sets.

Closed sets and open sets, or finite and infinite sets.

Closed sets and open sets, or finite and infinite sets.

No, it is not.