Numbers

# What operation are closed for integers?

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## Related Questions

You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).

No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.

There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division.

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 &#8450; (Complex numbers), &#8477; (Real Numbers), &#8474; (Rational Numbers) and &#8484; (integers) are closed under subtraction. &#8484;+ (the positive integers), &#8484;- (the negative integers) and &#8469; (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.

Yes, the set of integers is closed under subtraction.

I am not sure there are any fundamental operations of integers. The fundamental operations of arithmetic are addition, subtraction, multiplication and division. However, the set of integers is not closed with respect to division: that is, the division of one integer by another does not necessarily result in an integer.

-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.

negetive integers are not closed under addition but positive integers are.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

The set of integers is not closed under multiplication and so is not a field.

A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.

Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.

Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.

The set of rational numbers is closed under division, the set of integers is not.

Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/

Unfortunately, the term "whole numbers" is somewhat ambiguous - it means different things to different people. If you mean "integers", yes, it is closed. If you mean "positive integers" or "non-negative integers", no, it isn't.

A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)

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.

Any time you add integers, the sum will be another integer.

Yes it is : a + b = b + a for all integers a and b. In fact , if an operation is called addition you can bet that it is commutative. It would be perverse to call an non-commutative operation addition.

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