I figure out how to rebut your post, so i'll make a new reply again.
You previously say: A person who thinks a god does not exist is absent of a belief that God does exist. You further clarify "a god" is refer to "any god".
What is the amount to this "any god"?
1 god? 2 gods? 100 gods? Some gods? Many gods? All gods?
There's where i have to use "a person who believe at least one god exist", which the belief that at least one god exist, is enough to identify the person as a theist. Even another person believe multiple gods exist, he still believe at least one god exist, which can be identify as a theist.
And as long as a person absence the belief that at least one god exist, he then is not a theist. Which is my definition for atheist.
And i have to use "a person who believe no god exist" to be a part of definition for strong atheist. Which if there are two atheists, they both absence the belief that at least one god exist, the first person believe no god exist, the second person absence the belief that no god exist.
They are both atheist because they fit with the definition of atheist, which is absence the belief that at least one god exist.
The presence of belief that no god exist make the first person also a strong atheist.
The absence of belief that no god exist make the second person also a weak atheist.
Atheist, strong atheist, weak atheist, theist
Again, your "a god", "any god", haven't specify the number you refer to the god.
It can be 1 god, 2 gods, 100 gods, some gods, many gods, all gods, you have to clarify the number, otherwise that is too vague.