I+ = I- = 0
This is correctly stated as a property of an ideal op-amp. It's roughly true as long as the input voltage stays within the normal operating range (and particularly if the input voltage doesn't go outside the power supply rails). And as long as we don't care about very small currents, in the range of microamps down to femtoamps depending on the op-amp.
V+ = V-
This is not a property of an ideal op-amp.
The property you're thinking of is
If the gain is infinite, and we have a negative feedback configuration, then it will work out that the input voltages are driven to be equal. But if an ideal op-amp is used as a comparator, for example, the inputs will not be equal.
The infinite gain property is limited in real op-amps first because real gains are typically only 10,000 to 100,000. Also, the output voltage of real op-amps can only swing within a limited range. The most this could be is from the lower power rail to the upper power rail, but often it's 1 or 2 volts less on either side.