The int type in python offers two attributes named numerator and real that have the same content as __int__(). 
As all of these 3 values returns the same internal attribute, I guess real is a property like:
@property
def real(self):
   return self.__int
However I cannot find this hidden property dir dir or either a = int(); a._int__<tab> in IPython. 
So I looked at the source code and found this:
static PyGetSetDef int_getset[] = {
    {"real",
     (getter)int_int, (setter)NULL,
     "the real part of a complex number",
     NULL},
    {"imag",
     (getter)int_get0, (setter)NULL,
     "the imaginary part of a complex number",
     NULL},
    {"numerator",
     (getter)int_int, (setter)NULL,
     "the numerator of a rational number in lowest terms",
     NULL},
    {"denominator",
     (getter)int_get1, (setter)NULL,
     "the denominator of a rational number in lowest terms",
     NULL},
    {NULL}  /* Sentinel */
};
And this:
static PyObject *
int_int(PyIntObject *v)
{
    if (PyInt_CheckExact(v))
        Py_INCREF(v);
    else
        v = (PyIntObject *)PyInt_FromLong(v->ob_ival);
    return (PyObject *)v;
}
But this the furthest I can go by myself.
Where the actual value of an integer is stored inside an integer instance?
The main reason for this question is that I want to extend the float type with a MyFloat where I would like to refer to the value of the instance. 
The actual integer value is in ob_ival. In essence, int_int is simply taking the integer value from one int object and wrapping it in another object.
Not sure why you can't see the properties. If I run this, they show up for me, in both 2.7 and 3.4 versions:
x = 8
dir(x)
EDIT: Too hard to explain in a comment, so adding to the answer.
You could easily subclass it like this:
class foo(int):
    def __getitem__(self):
        return self + 1
foo(8).__getitem__()
You could also use super to explicitly access the int object this way. 
(You do realize that __getitem__ is for use with keyed objects [dict-like, say] and hence normally gets a second argument specifying the key, right? And int and float are not keyed.)
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