Why can perfect fluids have different layer velocities without shear stress?

[better361]

So the textbook I am reading says that a perfect fluid cannot sustain shear stress, or that $$p_{yx}=2\mu \dot \epsilon_{yx} =0$$, where $\mu$ is the viscosity, and $\dot \epsilon_{yx}$ is the rate of angular deformation. Then it says when $\dot \epsilon_{yx} =0$, this means that "two adjacent horizontal layers of a perfect fluid can move at different velocities without one layer affecting the other layer through internal resistive stresses." This seems to me, however, like what would happen if the viscosity were zero.

Can someone clear up my misconception?

 

[Orodruin]

Viscosity is zero in a perfect fluid. The situation described is not $\dot\epsilon_{xy}=0$ but $\neq 0$.

Edit: Why is \eps not a standard TeX command yet?

 

[better361]

I think ideal fluids are a subset of perfect fluids, at least according to my book.