[c++] operator << must take exactly one argument

A friend function is not a member function, so the problem is that you declare operator<< as a friend of A:

 friend ostream& operator<<(ostream&, A&);

then try to define it as a member function of the class logic

 ostream& logic::operator<<(ostream& os, A& a)
          ^^^^^^^

Are you confused about whether logic is a class or a namespace?

The error is because you've tried to define a member operator<< taking two arguments, which means it takes three arguments including the implicit this parameter. The operator can only take two arguments, so that when you write a << b the two arguments are a and b.

You want to define ostream& operator<<(ostream&, const A&) as a non-member function, definitely not as a member of logic since it has nothing to do with that class!

std::ostream& operator<<(std::ostream& os, const A& a)
{
  return os << a.number;
}

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