运算符重载[]是否也会自动重载算术？

Question

说我有一个MyOwnArray班，顾名思义，我想自己做一个   数组。我发现可以通过运算符重载来返回索引值。

#include <iostream>
using namespace std;

class MyOwnArray {

private:
    int arr[3];

public:
    MyOwnArray() {
        arr[0] = 1;
        arr[1] = 2;
        arr[2] = 3;
    }

    int &operator[](int i) {    // Also overload +, +=, etc?
        return arr[i];          // and I'm only returning the value
                                // but it seems to modify when using "+="
                                // as demonstrated in main()
    }

};


int main() {

    MyOwnArray a;       // my own array

    cout << a[0];       // outputs "1".
    a[0] += a[2];       // Not expecting this to work, but it does
    cout << a[0];       // outputs "4"

    return 0;
}

我期望cout << a[0]输出值1。 我没想到我会做类似a[0] += 1的事情。操作符重载[]是否也自动重载算术运算？ 最重要的是：为什么我只返回以下内容时为什么a[0]被修改了？ 这个功能？

int &operator[](int i) {    // Also overload +, +=, etc?
        return arr[i];          // and I'm only returning the value
                                // but it seems to modify when using "+="
                                // as demonstrated in main()
}