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c++ - difference between global operator and member operator

Is there a difference between defining a global operator that takes two references for a class and defining a member operator that takes only the right operand?

Global:

class X
{
public:
    int value;
};

bool operator==(X& left, X& right) 
{
    return left.value == right.value;
};

Member:

class X
{
    int value;
    bool operator==( X& right) 
    {
        return value == right.value;
    };
}
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One reason to use non-member operators (typically declared as friends) is because the left-hand side is the one that does the operation. Obj::operator+ is fine for:

obj + 2

but for:

2 + obj

it won't work. For this, you need something like:

class Obj
{
    friend Obj operator+(const Obj& lhs, int i);
    friend Obj operator+(int i, const Obj& rhs);
};

Obj operator+(const Obj& lhs, int i) { ... }
Obj operator+(int i, const Obj& rhs) { ... }

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