Why is the result value of the compare operation different for the mathematically same formula in cpp?

I’m having trouble comparing size of vector and simple constant -1

I think both

• (index >= (arr.size() - 1))
• ((index + 1) >= arr.size())

are logically same.

However, the first one returns 1 not 0.
What’s the difference between two comparation?

#include <iostream>
#include <vector>

using namespace std;

int main() {
  int index = -1;
  vector<char> arr(6);
  cout << (index >= (arr.size() - 1)) << endl;
  cout << ((index + 1) >= arr.size()) << endl;
}

>Solution :

The arr.size method returns an unsigned integer type, so the type of the right-hand side of the comparison is unsigned. This results in the left side being converted to unsigned.

When the value on the left is -1, this gets converted to a very large unsigned number, resulting in the first comparison being true. In the second case, the value on the left is 0 so it doesn’t change when being converted to an unsigned type and the comparison is false.