As we have seen it is best considered as input parameter directly input differential voltage vD rather than the individual voltage inputs present at the poles V+ and V-.
There is also another aspect that should be considered to complete the mathematical model of the Operational Amplifiers.
What does happen when the model return a value exceeding the range of the power supply voltages?
Let assume that power supply voltages are:
and let assume that inputs are:
In this case differential voltage input is equal to:
and voltage output is equal to:
The output voltage exceeds VCC!
Is it possible?
Certainly it isn't.
What happens is that voltage output VOUT can not exceed VCC or VEE (it doesn't even reach them, but the difference is small and we assume that VOUT's limits match exactly to VCC and VEE).
The mathematical model changes and the curve becomes: