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

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βˆ™ 2017-11-27 12:53:15
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Q: Why the set of odd integers under addition is not a group?
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Related questions

Under which operation is the set of odd integers closed?

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.


ARe odd integers not closed under addition?

That is correct, the set is not closed.


Why are odd integers closed under multiplication but not under addition?

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


What is index in group theory?

Say we have a group G, and some subgroup H. The number of cosets of H in G is called the index of H in G. This is written [G:H].If G and H are finite, [G:H] is just |G|/|H|.What if they are infinite? Here is an example. Let G be the integers under addition. Let H be the even integers under addition, a subgroup. The cosets of H in G are H and H+1. H+1 is the set of all even integers + 1, so the set of all odd integers. Here we have partitioned the integers into two cosets, even and odd integers. So [G:H] is 2.


Are odd numbers closed under subtraction?

No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.


What the probability of an odd number?

The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.The answer depends on what set of integers is under consideration.


Is the set of odd integers closed under division?

No. For example, 5 is an odd integer and 3 is an odd integer, yet 5/3 is neither an integer nor odd (as odd numbers are, by definition, integers).


Why is an odd number times an odd number an odd number?

Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1 Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k. Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.


Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?

1 No. 2 No. 3 Yes.


Are odd numbered sets closed under addition and multiplication?

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.


Is the set of odd numbers closed under addition?

no

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