Here's a little question to test your definition:
A test point on an electrical circuit has a voltage which varies between 5V and 7V, and this variation is random. It contains no data or patterns. Over the long term the random variations are centred around 5V, so they contain no DC offset. Think of it as noise, if you will.
At this test point, is the signal AC or DC?
Well it isn't moving between two values, so the dictionary definition of "alternating" doesn't apply. No polarity reversals take place, so it doesn't meet my definition of alternating, either. Also, I'm certain that "moving around at random" is not part of any dictionary definition of "alternating".
So: can something moving around at random be described as "alternating"? That word implies alternates: that is, two or more identifiable values. It does not seem to imply an infinite number of alternates, because then they wouldn't be alternates.
I'm just trying to suggest that applying a one-word label to my example doesn't work. It is neither DC nor AC, and arguing the toss is pointless. It is something like: "6V DC with 2V p-p random noise added", or possibly "A voltage varying at random over all possible values between 5V and 7V". The description cannot be reduced any further.
I deliberately said the signal contained a random element because I wanted to test the definition of "alternating ". Does alternating include "random"?
Putting that aside.....
If we simplify it by having a 2V p-p sine wave added to 6V DC, is the signal now AC or DC? I still argue that you cannot apply either label alone because it clearly contains aspects of both. I did mention earlier that instead of AC and DC we could legitimately refer to "the AC component" and "the DC component". This is much better because it embraces the the observed phenomenon more completely: the signal comprises two components summed: 6V DC and 2V p-p AC.
To summarise: I suggest that a voltage varying sinusoidally between 5V and 7V should not be described as DC or AC. Rather, it should be described as having both a DC component (6V DC) and an alternating component (2Vp-p AC), and the actual signal is the sum of the two components.
No more need to argue about what counts as DC and what counts as AC.