According to one wiki source, the 'a' prefix doesn't mean "no" but rather "not" or "an absence of".
If you have an absence of something, it means there's
none of it. And frankly, I took Ancient Greek for five years in secondary school; even if my definition were at odds with What Some Bloke On Wikipedia Wrote, I'm not prepared to defer to that. Heck, it's Wikipedia, give me five minutes and I'll make it say what I want it to. Moreover, what you're trying to do is taking the English translations of elements of a Greek word, and then applying them to each other according to the rules which govern the English language, rather than those which govern Greek.
Thus, "atheist" is not "no theism" but "not theism", a difference which is subtle but important.
The distinction exists, yes, but your conclusion doesn't follow from your premises (even if those were correct, which they're not). As I noted previously, the distinction depends on whether the "a-" reflects on "theism" part, or just the "theos" part.
And is it really important? Nowadays, "atheism" is used to mean both "no god-ism" (so-called "strong" atheism) and "not-godism" ("weak" atheism) and I have no issue with that. I just think your claim that the original meaning is "not-godism" isn't supported by the evidence.
Strong atheism = weak logic. You are indeed arguing from ignorance. You have no basis to conclude there is no god(s) nor will there ever be, considering you have not surveyed all of space and time (if you did that, you'd be the god, thus disproving your own hypothesis).
And once again, this canard gets trotted out. As has been pointed out time and time and time again in this forum, that argument only works if you wield a definition of the term "god" which is watered down to such an extent that it bears zero practical resemblance to the way it is used everywhere except in this kind of forum, and more specifically, in this particular (piss-poor excuse for an) argument.
It is like I may or may not have an object in my desk drawer. You haven't seen it, and the drawer might be locked only to you. Therefore you conclude that any object cannot exist in the drawer (and then have the gall to claim that that is the default position).
It is like you claim to have a twelve-inch ruler locked in your desk drawer. I cannot get into the desk drawer to verify its presence, but I
can measure its outer dimensions, and find it measures 8" x 8". Applying the Pythagorean theorem, I conclude that it is physically impossible for a straight 12-inch piece of rigid material (such as wood, metal or plastic, the most common materials used in making rulers) to fit inside the drawer, and I tell you so. You respond by saying that the object is not necessarily straight or rigid, and that you're not using Imperial inches (though you won't specify which type of inch you
are using). In other words, the object in your drawer does not have all of the characteristics, and may indeed have
none of the characteristics, of the kind of object to which people commonly refer when they speak of a "twelve-inch ruler."
There may or may not be an object of some indeterminate nature in your drawer, and I can't prove there isn't. But since the question was whether there is specifically a twelve-inch ruler in your drawer, that's beside the point. As is your "argument."