Why is numeric_limits::infinity() misbehaving logically for integral types

Question

std::numeric_limits<T>::infinity() function is logically misbehaving for integral types but for double its working fine. Is there some reason for defining such behavior in standard library, which returns 0 instead of builtin_huge value in case of integral types?

#include<iostream>
#include<limits>

int main() {    
    std::cout << std::boolalpha;

    std::cout << (9 < std::numeric_limits<int>::infinity()) << std::endl; // returns false
    std::cout << (9 > std::numeric_limits<int>::infinity()) << std::endl; // returns true

    std::cout << (9 < std::numeric_limits<long>::infinity()) << std::endl; // returns false
    std::cout << (9 > std::numeric_limits<long>::infinity()) << std::endl; // returns true

    std::cout << (9 < std::numeric_limits<double>::infinity()) << std::endl; // returns true
    std::cout << (9 > std::numeric_limits<double>::infinity()) << std::endl; // returns false
}