@IRFRANK,
Yeah, it's as simple as that. There are those who will assert (with no good reason) that the word is a modern construction, and then attempt to imply that the idea is a modern construction. That's simply not true. From the Wiktionary entry on
:atheos
Alternative forms
atheus
Etymology
From Ancient Greek ἄθεος (atheos, “godless, without a god”).
Noun
atheos (genitive atheī); m, second declension
an atheist, term applied to those who thought to reject the gods worshipped by the larger society.
This was already pointed out in this thread. The idea goes back at least thousands of years. That's all that atheist means, without god. Those who have an agenda, usually to discredit atheists and "atheism" will make other claims, but the historical record is against them.
Your definition, which suggests that atheists are those who deny that there is or can be a god, plays into the hands of the silly, militant agnostics who wish to assert their intellectual and moral superiority (we had a long-running thread in which agnostics, notably Frank, made just that claim) need for atheist to mean someone who denies that there are any gods. Theists prefer that definition as well, because they want to create an antagonistic dichotomy. Those of us who have been atheists all of our adult lives, however, know that most atheists simply don't believe and usually don't care. These are the implicit atheists, the skeptical atheists, the so-called "weak" atheists.