answersLogoWhite

0


Best Answer

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

User Avatar

Wiki User

โˆ™ 2018-05-01 11:05:44
This answer is:
User Avatar
Study guides

Algebra

20 cards

A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

โžก๏ธ
See all cards
3.81
โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…
1765 Reviews

Add your answer:

Earn +20 pts
Q: Why is a set of positive integers not a group under the operation of addition?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Other Math

Is the set of all negative integers a group under addition?

no


What groups are subsets of integers?

Integer Subsets: Group 1 = Negative integers: {... -3, -2, -1} Group 2 = neither negative nor positive integer: {0} Group 3 = Positive integers: {1, 2, 3 ...} Group 4 = Whole numbers: {0, 1, 2, 3 ...} Group 5 = Natural (counting) numbers: {1, 2, 3 ...} Note: Integers = {... -3, -2, -1, 0, 1, 2, 3 ...} In addition, there are other (infinitely (uncountable infinity) many) other subsets. For example, there is the set of even integers. There is also the subset {5,7}.


Why the set of odd integers under addition is not a group?

Because the set is not closed under addition. If x and y are odd, then x + y is not odd.


0 belongs to what family of real numbers?

0 belongs to the reals. It is a member of the irrationals, the rationals. It is also a member of the integers; It is a member (the identity) of the group of even integers, 3*integers, 4*integers etc with respect to addition.


Examples to prove the set of integers is a group with respect to addition?

In order to be a group with respect to addition, the integers must satisfy the following axioms: 1) Closure under addition 2) Associativity of addition 3) Contains the additive identity 4) Contains the additive inverses 1) The integers are closed under addition since the sum of any two integers is an integer. 2) The integers are associative with respect to addition since (a+b)+c = a+(b+c) for any integers a, b, and c. 3) The integer 0 is the additive identity since z+0 = 0+z = z for any integer z. 4) Each integer n has an additive inverse, namely -n since n+(-n) = -n+n = 0.

Related questions

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

No. It is not a group.


What is the symbol for integers?

negative is - Positive is + The group of integers is represented by ℤ.


Is the set of negative integers a group under addition?

Is the set of negative interferes a group under addition? Explain,


Is the set of all negative integers a group under addition?

no


Does the set of even integers form a group under the operation of multiplication?

No. The inverses do not belong to the group.


What is the differences between positive and negative integer?

Positive integers are greater than zero, negative integers are less than zero. The set of positive integers is closed under multiplication (and form a group), the set of negative integers is not.


What groups are subsets of integers?

Integer Subsets: Group 1 = Negative integers: {... -3, -2, -1} Group 2 = neither negative nor positive integer: {0} Group 3 = Positive integers: {1, 2, 3 ...} Group 4 = Whole numbers: {0, 1, 2, 3 ...} Group 5 = Natural (counting) numbers: {1, 2, 3 ...} Note: Integers = {... -3, -2, -1, 0, 1, 2, 3 ...} In addition, there are other (infinitely (uncountable infinity) many) other subsets. For example, there is the set of even integers. There is also the subset {5,7}.


Example of group is an abelian group?

The set of integers, under addition.


Give two reason for the set of odd integers is not a group?

Assuming that the question is in the context of the operation "addition", The set of odd numbers is not closed under addition. That is to say, if x and y are members of the set (x and y are odd) then x+y not odd and so not a member of the set. There is no identity element in the group such that x+i = i+x = x for all x in the group. The identity element under addition of integers is zero which is not a member of the set of odd numbers.


What are the rules of integers?

To start with, the set of integers is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element. This Group, Z, satisfies four axioms: closure, associativity, identity and invertibility. that is, if x , y and z are integers, thenx + y is an integer (closure).(x + y) + z = x + (y + z) (associativity)there is an integer, denoted by 0, such that 0 + x = x + 0 = xthere is an integer, denoted by -x, such that x + (-x) = (-x) + x = 0.In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative: x + y = y + x) and it has a second binary operation (multiplication) that is defined on its elements. This second operation satisfies the axioms of closure, associativity and identity. It is also distributive over the first operation. That is,x*(y + z) = x*y + x*z


Why the set of odd integers under addition is not a group?

Because the set is not closed under addition. If x and y are odd, then x + y is not odd.


0 belongs to what family of real numbers?

0 belongs to the reals. It is a member of the irrationals, the rationals. It is also a member of the integers; It is a member (the identity) of the group of even integers, 3*integers, 4*integers etc with respect to addition.

People also asked

What did John Locke believe would happen without a government?

View results

What is verbal irony?

View results

Describe what happens during Prophase?

View results

Who wrote Raindrops keep falling on my head?

View results