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In the additive group of integers, the order of every elements a ≠ 0 is
- a)infinity
- b)one
- c)zero
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In the additive group of integers, the order of everyelements a ≠ 0...
The correct answer is:
1. infinity
In the additive group of integers, the order of an element aaa (where a≠0 ) refers to the smallest positive integer nnn such that n⋅a=0 However, for any non-zero integer aaa, there is no positive integer nnn that satisfies this equation because adding aaa to itself any number of times will never result in 0. Therefore, the order of any non-zero element in this group is infinite.
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In the additive group of integers, the order of everyelements a ≠ 0...
In the additive group of integers, the order of every element a is infinite. This means that for any integer a, there is no positive integer n such that na = 0, where 0 is the additive identity element.
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In the additive group of integers, the order of everyelements a ≠ 0...
By definition :- the order of additive group is positive integer n s.t na=0, where a is non zero elements of additive group of integer.
We have only two case which is satisfied given condition.
fist is n=0 & second is n is infinite
but fist case is impossible so order of nonzero elements of additive group is infinite..
We have only two case which is satisfied given condition.
fist is n=0 & second is n is infinite
but fist case is impossible so order of nonzero elements of additive group is infinite..
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