set theory - Set comprehension when the condition is false

The Cartesian product of two empty sets is the singleton set ${ () }$ containing the empty tuple. So, given a set $A$ which is empty, $A times A$ is defined as: $$A times A = { (a,a) mid a in A } = { () }$$ Now, does that mean that $()$ satisfies the condition $a in A$? And if so, why don't we include the empty tuple in the Cartesian product of non-empty sets?

(It would be nice if you point out which concept I mis-understand: the set comprehension, or the tuple.)

Thanks in advance.

[edit: I should add the following link: Wikipedia: Empty_product#Nullary_Cartesian_product]

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