Test Dynamic Memory

I notice that some codes do not have to test dynamic memory to
determine if dynamic memory is available or not. It is said in Deitel
How to Program C++ book.

Is it necessary to test dynamic memory if memory is very small like
less than 256 bytes? The test should fail and prevent you from doing
class constructor.

array class is already constructed before dynamic memory is tested.
If it fails, error message is displayed before exit() function
terminates the program. If I decide to allow the program running
after dynamic memory reported out of memory, then array class should
use destructor to clean up all data members and release array class
from the memory.

For example:

class array
{
public:

    array( int size )
    {
        m_pArray = new int[ size ];
        m_size = size;

        if( m_pArray == 0 )
        {
            // Display Error Message -- out of memory
            // Close other application and try again or
            // use exit() function

            // if( yes )
            // exit();
            // else ( no and continue )
            m_bOutofMemory = true;
            return;
        }
    }

    ~array()
    {
        if( m_pArray != 0 )
        {
            delete [] m_pArray;
            m_pArray = 0;
        }
    }

    bool TestMemory()
    {
        return m_bOutofMemory;
    }

private:
    int m_size;
    int *m_pArray;
    bool m_bOutofMemory;
};

int main()
{
    array *a = new array( 5 );
    if( a->TestMemory() == true )
        delete a;

    // Continue the program after
    // exit() function is not invoked.

    system( "pause");
    return 0;
}