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## Main Question or Discussion Point

I'm reading Riley's "Mathematical Methods for Physics and Engineering" and I came across this expression about vector spaces:

"A set of objects (vectors)

What I don't understand is: what does commutative and associative addition have to do with a closed set?!

"A set of objects (vectors)

**a, b, c, ...**is said to form a*linear vector space V*if the set is closed under commutative and associative addition (...)"What I don't understand is: what does commutative and associative addition have to do with a closed set?!