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I know that a Group G is defined as a set of elements with a binary operation with these three properties:
2) Inverses Exist
3) Identity Exists
However there are many definitions such as the one found on wikipedia that say closure is also a property and what not. However I have seen some other things about groups and it said closure is not included as a property, mainly Harvard Abstract Algebra videos on Youtube. I know that closure can come from those three properties sometimes, but not all the times. So my question is, is closure a property of a group?
I believe it is because there has been more information supporting it being one, then it not being included.