You fumbled.
active belief includes your declaration.
Children cannot actively participate in disbelief.
They would need the word .....god....in their vocabulary......AND
the decision to say 'nay'.
No declaration has to be made at all - that is the whole point.
Read it again.
0 is the null state (People who make no declarations)
1 is a positive state. (Theists)
-1 is an inverse response to 1. (Active "declaring" atheists)
In order to be considered an active theist, there must be a positive state (a declaration of 1).
Anything that is not a positive state (the null state or the negative state) can be considered atheistic, as they are not positive declarations. So all people who are not 1s are atheists to one degree or another.
There is a big difference between 0 and -1, certainly. But neither 0 nor -1 are the same thing as 1...
Therefore, all people who are not actively proclaiming 1 are, mathematically, not 1. They are either null or negative 1.
There should be no arguing here. It's so incredibly simple.
This works out the same way in other scenarios:
People either have milk in their glass or they do not. (Theists)
Someone with milk in their glass can be said to be drinking milk.
Someone with coke instead of milk cannot be said to be drinking milk and, quite obviously, is drinking something opposite of milk. (Active "declaring" atheists)
Both the coke drinker and the milk drinker are in a different state than the person with an empty glass - but in no way shape or form can the person with the empty glass be said to be drinking milk...
Therefore, since the person with the empty glass cannot be said to be drinking milk (thus disqualifying them from being labeled as a theist) their default label is that of "atheist", meaning WITHOUT THEISM.