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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..
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.
yeah you are right but in case finitly generated group .. but here it is infinitly generated cyclic group..
its generators are two.
feel free to ask again
so my definition for generator is true only for finite groups right?
your definition is correct for finitely generated cyclic group not for infinitely generated cyclic group
feel free to ask again