I will absolutely buy what you said, but understand the import of what
you're saying....you're saying that the language of "AC" and "DC" has
essentially been somewhat *******ized from its original meanings to
also mean zero-frequency and non-zero-frequency signals. Therefore, to
describe a 10Vpp signal with a 10VDC offset as an "AC" signal is
actually contrary to the original connation of "alternating current"
since it (net) results in a signal which yields only a mono-directional
(i.e. direct) current flow (albeit time variant). So in a sense, you
could say I am holding "pure" to the original (circa 1890's) definition
of AC/DC while its use has been "officially" corrupted to cover the
concepts of "zero frequency" and "non-zero-freuency".

Agree?