Is permittivity of pec INFINITE?

I saw an article talking about the permittivity of a highly conductive material is very large and infinite for the perfect conductor.

The following is from efunda.com

"In general, good conductors such as metals have an essentially infinite permittivity. Finite permittivities are normally associated with dielectric materials that have bound internal charge. Much of the internal charge of metals are free to roam, and will do so in the presence of an external electric field to cancel the electric field within the metal. Hence, metals (such as silver, copper, and gold) polarize extremely strongly and thereby have an infinite permittivity."

However, in EM books, e.g., Cheng-field and wave electromagnetics, the relative permittivity is considered as 1, that is the permittivity is same to e0=8.85e-15.

Also in HFSS, the relative permittivity values of well-known conductors, copper-silver-..., are all assigned to 1.

Which one is right?

Am I confused because one is talking about the complex permittivity and the other only concerns the real part?

Perfect conductors don't have finite permittivity. The reason is that explained by you. Could you, please, report the exact phrase you read on the cited book ?

If you define λ as the inverse of ε.

λ = 1/ε

and if you take the limit of λ

You will find that the phase of λ is undifined.

1. According to the second curl equation:
curl×H=jωεE+σE
as σ becomes large we can have the approximation;
curl×H≈σE
for PEC, σ=∞ so the approximation becomes fully accurate, no matter what the ε is.

2. But if you consider complex permittivity;
curl×H=jωεE, where ε=ε'+σ/jω
for PEC it becomes purely imaginary and infinite