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The + symbol doesn't denote any particural operation mathematics. it widely used for vector space where commutativity is a condition though.

A symbol's property depend on the operation, the multiplication symbol for example is commutative in some cases and not in others.

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It is a convention, not a rule, in mathematics to use (+) to represent operations that are commutative (i.e. abelian) groups.

But this convention is not at all respected in programming (e.g. + for string concatenation in many languages) so I have to admit that it's pretty irrelevant.

The war to keep programming operators at all consistent with mathematics was lost long ago, with `=` and `==` being the worst offenders.

To be fair, mathematics uses = to indicate assignment as well, e.g. for summation limits.

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