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If it's infinite it doesn't much matter whether you are talking about absolute or relative permittivity, does it.
Think about what permittivity (or dielectric constant) physically means. It describes the degree to which an applied electrostatic field induces a counter polarization field within a material (usually a dielectric but dielectrics are simply on a continuum with semiconductors and metals).
Then think about what allows a metal to be a conductor, namely that metals have carrier concentration so high and with such high mobility that they equalize charge disparities at a significant fraction of the speed of light (such that voltage is nominally the same on two end of a metal wire, for example).