The book is clearly imprecise! An ideal opamp puts out:
- 0V when both inputs are perfectly equal, at any voltage level;
- Plus `infinity' volts when the positive input is greater than the negative one;
- Minus `infinity' volts when the positive input is lower than the negative one;
The last two ensures that feedback actually works, both positive and negative.
The other properties seems ok, it doesn't source or sink from either input (whatever the potential is) and it can source or sink an infinite amout of current without deviating from its infinite output (it's really infinite, in voltage and current)
If you are talking about input impedences then you need to state that the input impedance is infinite both between the input terminal and the ground and between the terminals. This is useful since real amps have both common mode and differential mode impedances
Removing the infinite current/voltage properties creates a lack of linearity i.e. superposition doesn't work anymore and most other theorems too.
Removing the requirement for zero output impedance and infinite input impedance complicates analysis (at least it's still linear)
Removing the infinite gain doesn't really make you lose linearity but forces you to consider the working point (which is what the GBWP is in reality)
If it was as the book said i.e. the potential between inputs it's alway zero then (by definition) the differential mode impedence would be zero i.e. they would be shorted together. That's not really the case.
What they wanted to say is the `virtual ground' property where to have the output zero both input must be at the same potential (and since the output would be otherwise infinite, it's the only acceptable working point)