Below example should clarify all:
When a scientist/mathematician says
xxxx"X=4"
Then this implies there is absence of
xxxx"1, 2, 3, 5, 6, 7 etc"
When an Atheist says
xxxx"Atheism = lack of belief in God",
Then this implies there is absence of
xxxx"good, bad, etc" in Atheism
Or as others sometimes say "I do NOT want to be put in a box"
To claim "I am an Atheist (or Hindu/Christian for that matter) means you put yourself in a box"
This does really clarify the point of the thread. You have to put logic as far away from the original intent of the thread as possible.
An even poorer analogy. The logic of Math has nothing to with 'belief or non-belief in God.
Though you did change things, which comes closer to reality. You correctly "good, bad, etc," but atheism does not imply the "absence ot . . ." Poor choice of words. Atheism does not imply the "absence nor the presence of good or bad, etc." Atheism only implies the absence of God(s).