Counting.

Oh you know how you classify the amount of objects by counting. Well how about finding the relationships between numbers, that might be useful. I'll start.

If you have 1 apple and 1 apple and count them you get 2, how should we define this process using simple symbols and terms?

a ADD a EQ aa

come to think of it...
aa ADD aa EQ aaaa
AND
a ADD a ADD a ADD a EQ aaaa
and since aa EQ a ADD a, the equation aa ADD aa EQ aaaa EQ :-a ADD a-: ADD :-a ADD a-: EQ aaaa

I think this could go places