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?

s(1)=2

Needs more Curry.

0 = {}
1 = {{}}
2 = {{},{{}}}

etc.

You're pairing the set of apples that you are counting with the set of natural numbers.

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

>>6


actually, that last part was a tad confusing
aa ADD aa EQ aaaa EQ :-a ADD a-: ADD :-a ADD a-: EQ aaaa

should have been written clearer as
:-aa ADD aa EQ aaaa: EQ :-:-a ADD a-: ADD :-a ADD a-: EQ aaaa-:

I got it

F(x)dwTz:{F((x))dwTz:::}^F(y)dxTv:[F[[x]]dxTv:::]~1*&*F(x)dwTz:{F((x))dwTz:::}^Y(z)dyTb:[F[[y]]dyTb:::]~1->TWO-APPLES