A binary operation on a set is closed on the set by definition. If an operation isn’t closed, then it isn’t considered a binary operation on that set. Of course

A binary operation on a set is closed on the set by definition. If an operation isn’t closed, then it isn’t considered a binary operation on that set. Of course, it doesn’t hurt to state the closure property explicitly. I have talked a bit more about it in a totally unrelated blog post here: https://susam.net/product-of-additive-inverses.html#closure-properties https://susam.net/product-of-additive-inverses.html#closure-...