(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I would define a group as follows:

A group consists of a non-empty set G together with a binary operation (say, *) on G such that the following axioms hold:

G1.....G2....G3...

2. Relevant equations

3. The attempt at a solution

I know this is a trivial question, but doesn't a binary operation on a set (here G) necesserily imply that the set is closed under that binary operation? The only reason i ask is that many of the definitions of groups I have come across include both that * is a binary operation under which G is closed. Isn't this redundant?

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# Definition of a group with redundancy?

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