I don't understand why the set of natural numbers constitutes a commutative monoid with addition, but is not considered an Abelian group.
Why is the set of natural numbers not considered a non-Abelian group?
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abstract-algebra
group-theory
abelian-groups
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1What is the additive inverse of $n\neq 0$? – 2012-12-07
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32It's not a nonabelian group. It's an abelian nongroup. – 2012-12-07
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1Note that $\mathbb N$ is not considered a group (even less an abelian group), but your question title suggests that it is considered a non-abelian group - no it isn't even a non-abelian group. – 2012-12-07
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0Such a "great" question deserves more than 3 upvotes! – 2012-12-09