I can feel your anger

[Skepsis]

Atheist motivating sets are necessarily atheistic.

What motivation can one get from "I don't believe there to be a God or Gods"?

You're trying to come up with some kind of foundationalism, where motivating sets have to be drawn from some base set of foundational beliefs (or something of the like), and since atheism has no foundational beliefs, it can't form a motivational set.

...
Wow. You got it.

Apparently, you think that this approach is so obviously correct that you don't need to think about what your own assumptions were in order to explain it to someone else, and that not automatically sharing your particular intuition for motivating sets is like not sharing your understanding of the English word "of". Cool beans.

I was under the impression that people aren't capable of acting on things that they don't believe in.

What I'm thinking of is a bit more general than that. Maybe there are no foundational beliefs; maybe there's just an infinite tower of beliefs. I don't want to pigeonhole myself into only one kind of set structure.

Now just keep doing what you always do: Abstract and abstract until all terms become mixed jumbles of useless dribble.
Theists are informed by a positive motivation.
Atheists cannot be motivated by anything based on their atheism; atheism is a lack of fucking belief in a God or Gods.

But most of what you're talking about is already handled, I think, by things like implication. "God created the universe" implies "God exists"; thus, if "God created the universe" is in the motivating set, then so must "God exists" (since we're really looking at the closure of the set under implication). This means that if we include q in the set of motivating beliefs, we include all beliefs necessary to believe q.

If A' was translated in the function A' B C', and the square root of q is S', then- Wait, what was q again?
Anyway, God exists, a positive claim, gives meaning to "God created the universe". I don't know what you were trying to say. Don't assign shit letters. Type it out. Unless it's short.

What I'm doing is more like, "Let's look at the motivating set. What are the characteristics of the motivating set?"

What is motivating about "I don't believe in God"? Seriously.

But the whole "cornerstone" approach is yours, not mine. Why is your approach better?

The "cornerstone" approach is yours- whether or not you understand what you're typing is a different story.
For theism and atheism to both be sets, as you suggest, they must share the capacity to give meaning to the subsets that are informed by the larger set. For something to "motivate" other things (looky there, your approach), that something must be the cornerstone of what is being motivated. Well, not exactly; the former about necessarily being the cornerstone is simply because if what is being informed (i.e. Christianity) must be primarily given meaning by the set (theism) or else the set could be more meaningfully labeled.