C++好友运算符重载不编译

#include <iostream>
#include <string>
class number
{
    public:
        friend std::ostream &operator << (std::ostream &s, const number &num);
        friend std::string  &operator << (std::string,     const number &num);
        friend std::istream &operator >> (std::istream &s,       number &num);
        friend std::string  &operator >> (std::string,           number &num);
    protected:
    private:
        void write (      std::ostream &output_target = std::cout) const;
        void read  (      std::istream &input_source  = std::cin);
        void to_string (      std::string &number_text) const;
        void to_number (const std::string &number_text);
};

std::istream & operator >> (std::istream &s,       number &num)
{
    num.read (s);
    return s;
}
std::string  & operator >> (std::string &s, number &num)
{
    num.to_number (s);
    return s;
}
std::string  & operator << (std::string &s, const number &num)
{
    num.to_string (s);
    return s;
}
std::ostream & operator << (std::ostream &s, const number &num)
{
    num.write (s);
    return s;
}

当我编译它时,我得到以下错误。。。

frag.cpp: In function ‘std::string& operator>>(std::string&, number&)’:
frag.cpp:17: error: ‘void number::to_number(const std::string&)’ is private
frag.cpp:27: error: within this context
frag.cpp: In function ‘std::string& operator<<(std::string&, const number&)’:
frag.cpp:16: error: ‘void number::to_string(std::string&) const’ is private
frag.cpp:32: error: within this context

有谁能帮忙吗;特别是为什么to\ n数字和to\ n字符串被认为是私有的,而读写是可以的?