Math and Arithmetic

# Is the set of positive integers a commutative group under the operation of addition?

No. It is not a group.

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## Related Questions

The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.

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

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

The commutative property holds for all numbers under addition, regardless of whether they are positive or negative - the sign of the number stays with the number, for example: -2 + 5 = (-2) + 5 = 5 + (-2) = 5 + -2 -2 + -5 = (-2) + (-5) = (-5) + (-2) = -5 + -2 Subtraction is not commutative, but when subtraction is taken as adding the negative of the second number, the commutative property of addition holds, for example: 5 - 2 &ne; 2 - 5 but: 5 - 2 = 5 + -2 = 5 + (-2) = (-2) + 5 = -2 + 5

The rules for addition are as follows:The sum of two negative integers is a negative integerThe sum of two positive integers is a positive integerThe rules for subtraction are as follows:If they are two positive numbers, do it normallyIf there is a negative and a positive ,change it to addition and switch the SECOND integer sign

diffrence will always be positive except when it is zero but is you speak of substraction operation it can be positive negative or zero

There are two properties of addition. The COMMUTATIVE property states that the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c. That is IT. No more! The DISTRIBUTIVE property is a property of multiplication over addition (OR subtraction), not a property of addition. The existence of of an IDENTITY and an ADDITIVE INVERSE are properties of the set over which addition is defined; again not a property of addition. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.

There are two properties of addition. The COMMUTATIVE property states that the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c. That is IT. No more! The DISTRIBUTIVE property is a property of multiplication over addition (OR subtraction), not a property of addition. The existence of of an IDENTITY and an ADDITIVE INVERSE are properties of the set over which addition is defined; again not a property of addition. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.

Integers are the positive and negative whole numbers with the addition of 0. The positive integers are the numbers 1, 2, 3, 4, 5, 6, etc. The negative integers are the numbers -1, -2, -3, -4, -5, -6, etc. 0 is neither positive or negative.any whole number that is positive, negative, or the number 0

Non-positive integers are zero and the negative integers.

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)

Addition isassociative: a + (b + c) = (a + b) + c and so both can be written as a + b + c without ambiguity,commutative: a + b = b + aThere are other properties, such as closure, identity and invertibility which depend on the domain over which addition is defined. For example, over the set of positive integers, there is no identity nor invertibility. If 0 is included, then there is an identity but still no invertibility.

The COMMUTATIVE property states that the order of the arguments of an operation does not matter. In symbolic terms, for elements a and b and for the operation ~, a ~ b = b ~ a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, for elements a, b and c, (a ~ b) ~ c = a ~ (b ~ c) and so, without ambiguity, either can be written as a ~ b ~ c. The DISTRIBUTIVE property is a property of two operations, for example, of multiplication over addition. It is not the property of a single operation. For operations ~ and # and elements a, b and c, symbolically, this means that a ~ (b # c) = a ~ b # a ~ c. The existence of an IDENTITY is a property of the set over which the operation ~ is defined; not a property of operation itself. Symbolically, if the identity exists, it is a unique element, denoted by i, such that a ~ i = a = i ~ a for all a in the set. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned. I have deliberately chosen ~ and # to represent the operations rather than addition or multiplication because there are circumstances in which these properties do not apply to multiplication (for example for matrices), and there are many other operations that they can apply to.

Some integers are positive numbers.Some integers are not positive numbers.Some positive numbers are integers.Some positive numbers are not integers.They are two sets whose intersection is the set of counting numbers.

Negative integers, zero and the positive integers, together form the set of integers.

No NEETs are counted using positive integers.No NEETs are counted using positive integers.No NEETs are counted using positive integers.No NEETs are counted using positive integers.

The set of integers includes negative integers as well as positive integers. It also includes the number zero which is neither negative nor positive.

Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.Then they are, simply, two different integers. Any two positive integers will do, according to the specification.

The pl sign for positive integers and the minus sign for negative integers.

* The quotient of two positive integers or two negative integers is positive. * The quotient of a positive integer and a negetive integer is negetive.

It means that given a set, if x and y are any members of the set then x+y is also a member of the set. For example, positive integers are closed under addition, but they are not closed under subtraction, since 5 and 8 are members of the set of positive integers but 5 - 8 = -3 is not a positive integer.

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