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Vijay posted an Question
October 08, 2020 • 02:06 am 30 points
  • IIT JAM
  • Mathematics (MA)

How can 1 be a generator for integers because when we add 1 to itself then we are always going to get positive integers and we are never going to get -integer

how can one be a generator for integers because when we add 1 to itself then we are always going to get positive integers and we are never going to get negative integers?

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    Deepak singh 1

    (Z,+) is abelian group , for generation of +ve numbers, 1 will generate and for -ve integers, -1 will generate .. that's why 1 and -1 are generators..

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    an element that generates the whole group itself is called a generator right? that is the definition of the generator. so 1 will only generate +ve integers hence 1 is not a generator. if my definition of the generator is wrong then, please correct me.

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    yeah you are right but in case finitly generated group .. but here it is infinitly generated cyclic group..

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    its generators are two.

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    feel free to ask again

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    so my definition for generator is true only for finite groups right?

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    your definition is correct for finitely generated cyclic group not for infinitely generated cyclic group

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    feel free to ask again

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